{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#4: Simplification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.1, Page number 4.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 1.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=10+(1/2);\n",
    "b=8+(1/2);\n",
    "c=6;\n",
    "d=7;\n",
    "e=6;\n",
    "f=4;\n",
    "\n",
    "#Calculation\n",
    "result=a-(b+(c-(d-(e-f))));\n",
    "\n",
    "#Result\n",
    "print \"result is\",result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.2, Page number 4.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 1.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=0.75;\n",
    "b=0.25;\n",
    "\n",
    "#Calculation\n",
    "#given question is (a*a)+(b*b)+(2*a*b) which can be solved using (a+b)**2\n",
    "result=(a+b)**2;\n",
    "\n",
    "#Result\n",
    "print \"result is\",result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.3, Page number 4.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 1.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=0.87;\n",
    "b=0.13;\n",
    "\n",
    "#Calculation\n",
    "Nr=(a**3)+(b**3);\n",
    "Dr=(a**2)+(b**2)-(a*b);\n",
    "result=Nr/Dr;\n",
    "\n",
    "#Result\n",
    "print \"result is\",result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.4, Page number 4.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 576.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=9840;\n",
    "b=410;\n",
    "\n",
    "#Calculation\n",
    "result=(a/b)**2;\n",
    "\n",
    "#Result\n",
    "print \"result is\",result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.5, Page number 4.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "required number is 70.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=40;\n",
    "b=30;\n",
    "c=10;\n",
    "\n",
    "#Calculation\n",
    "x=((a**2)-(b**2))/c;   #required number\n",
    "\n",
    "#Result\n",
    "print \"required number is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.6, Page number 4.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "required number is 3\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=3;\n",
    "b=4;\n",
    "c=6;\n",
    "d=9;\n",
    "\n",
    "#Calculation\n",
    "p=b+c-d;\n",
    "x=a**p;       #required number\n",
    "\n",
    "#Result\n",
    "print \"required number is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.7, Page number 4.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 2.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=2;\n",
    "b=math.sqrt(2);\n",
    "\n",
    "#Calculation\n",
    "c=1/(a+b);\n",
    "d=1/(b-a);\n",
    "result=a+b+c+d;\n",
    "\n",
    "#Result\n",
    "print \"result is\",result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.8, Page number 4.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 243\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "x=7;\n",
    "y=5;\n",
    "z=2;\n",
    "\n",
    "#Calculation\n",
    "xstary=((x+z)**2)*(y-z);\n",
    "\n",
    "#Result\n",
    "print \"result is\",xstary    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.9, Page number 4.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 1000.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=121;\n",
    "\n",
    "#Calculation\n",
    "m=math.sqrt(a);\n",
    "#since we are considering square root, value of n will be 2\n",
    "n=2;\n",
    "result=(m-1)**(n+1);    \n",
    "\n",
    "#Result\n",
    "print \"result is\",result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.10, Page number 4.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 1.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "k=1;\n",
    "x=3*k;\n",
    "y=4*k;\n",
    "\n",
    "#Calculation\n",
    "result=(6/7)+((y-x)/(y+x));\n",
    "\n",
    "#Result\n",
    "print \"result is\",result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.11, Page number 4.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 72.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "rootxminusrooty=1;\n",
    "rootxplusrooty=17;\n",
    "\n",
    "#Calculation\n",
    "#we get value of rootx and rooty by adding and subtracting the 2 equations\n",
    "rootx=(rootxminusrooty+rootxplusrooty)/2;\n",
    "rooty=(rootxplusrooty-rootxminusrooty)/2;\n",
    "result=rootx*rooty;\n",
    "\n",
    "#Result\n",
    "print \"result is\",result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.12, Page number 4.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 17.28\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=12;\n",
    "b=0.2;\n",
    "c=3.6;\n",
    "d=2;\n",
    "\n",
    "#Calculation\n",
    "x=a*b*c*d;\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.13, Page number 4.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 3.11\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=7;\n",
    "b=18;\n",
    "c=84;\n",
    "\n",
    "#Calculation\n",
    "x=((c/b)**2)/7;    \n",
    "\n",
    "#Result\n",
    "print \"result is\",round(x,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.15, Page number 4.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 3.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=256;\n",
    "b=2;\n",
    "\n",
    "#Calculation\n",
    "c=math.log(a)/math.log(b);\n",
    "x=math.log(c)/math.log(b);\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.16, Page number 4.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 9.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=13;\n",
    "b=2;\n",
    "c=4;\n",
    "\n",
    "#Calculation\n",
    "d=math.log(c)/math.log(b);\n",
    "e=d*b;\n",
    "x=(a-e);     \n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.17, Page number 4.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 6.0 *math.sqrt(3)\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=3*math.sqrt(27);\n",
    "b=math.sqrt(75);\n",
    "c=math.sqrt(12);\n",
    "\n",
    "#Calculation\n",
    "x=a-b+c;      \n",
    "\n",
    "#Result\n",
    "print \"result is\",x/math.sqrt(3),\"*math.sqrt(3)\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.19, Page number 4.11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 3 3/8\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "from fractions import Fraction\n",
    "\n",
    "#Variable declaration\n",
    "a=8+(1/4);\n",
    "b=8+(1/2);\n",
    "c=20+(1/8);\n",
    "\n",
    "#Calculation\n",
    "x=c-(a+b);\n",
    "y=x-int(x);\n",
    "\n",
    "#Result\n",
    "print \"result is\",int(x),Fraction(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.20, Page number 4.11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 9.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=math.sqrt(1296);\n",
    "b=2.25;\n",
    "\n",
    "#Calculation\n",
    "c=a*b;\n",
    "x=math.sqrt(c);\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.21, Page number 4.11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 95.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=124.9;\n",
    "b=63.15;\n",
    "c=65/100;\n",
    "\n",
    "#Calculation\n",
    "d=a-b;\n",
    "x=d/c;\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.22, Page number 4.11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 2.09090909091\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=17;\n",
    "aplusb=23;\n",
    "\n",
    "#Calculation\n",
    "b=aplusb-a;\n",
    "result=aplusb/(a-b);\n",
    "\n",
    "#Result\n",
    "print \"result is\",result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.23, Page number 4.12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 2.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=math.sqrt(24);\n",
    "b=math.sqrt(216);\n",
    "c=math.sqrt(96);\n",
    "\n",
    "#Calculation\n",
    "x=(a+b)/c;\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.25, Page number 4.12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 0.333333333333\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "x=5;\n",
    "y=-2;\n",
    "\n",
    "#Calculation\n",
    "result=(x-(2*y))**(1/y);\n",
    "\n",
    "#Result\n",
    "print \"result is\",result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.26, Page number 4.12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 20.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=2+(2/3);\n",
    "b=4/5;\n",
    "c=1/6;\n",
    "\n",
    "#Calculation\n",
    "result=a/(b*c);  \n",
    "\n",
    "#Result\n",
    "print \"result is\",result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.27, Page number 4.12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "value of 5/6 of 1/20 of 24 rupees is 1.0 rupee\n",
      "value of 4/7 of 14 of 2 1/4 kg is 18.0 kg\n",
      "answer given in the book is wrong\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=5/6;\n",
    "b=1/20;\n",
    "c=24;\n",
    "d=4/7;\n",
    "e=14;\n",
    "f=2+(1/4);\n",
    "\n",
    "#Calculation\n",
    "r1=a*b*c;     #value of 5/6 of 1/20 of 24 rupees(rupee)\n",
    "r2=d*e*f;     #value of 4/7 of 14 of 2 1/4 kg(kg)\n",
    "\n",
    "#Result\n",
    "print \"value of 5/6 of 1/20 of 24 rupees is\",r1,\"rupee\"\n",
    "print \"value of 4/7 of 14 of 2 1/4 kg is\",r2,\"kg\"\n",
    "print \"answer given in the book is wrong\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.28, Page number 4.12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 3.68181818182\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=11;\n",
    "b=2+(1/5);\n",
    "c=11/5;\n",
    "d=2+(1/2);\n",
    "e=2;\n",
    "\n",
    "#Calculation\n",
    "r1=a/b;\n",
    "r2=r1/c;\n",
    "result=(r2*d)-e;\n",
    "\n",
    "#Result\n",
    "print \"result is\",result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.29, Page number 4.13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 1.27777777778\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=2/3;\n",
    "b=1/5;\n",
    "c=1/10;\n",
    "d=4/5;\n",
    "e=1/8;\n",
    "f=1/2;\n",
    "\n",
    "#Calculation\n",
    "Nr=a+b-c;\n",
    "Dr=(d*e)+f;\n",
    "result=Nr/Dr;\n",
    "\n",
    "#Result\n",
    "print \"result is\",result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.30, Page number 4.13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 54.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=18;\n",
    "b=162;\n",
    "c=1;\n",
    "\n",
    "#Calculation\n",
    "x2=a*b*c;\n",
    "x=math.sqrt(x2);\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.31, Page number 4.13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 100.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=0.55;\n",
    "b=0.07;\n",
    "c=0.027;\n",
    "d=0.01;\n",
    "\n",
    "#Calculation\n",
    "Nr=(a**2)+(b**2)+(c**2);\n",
    "Dr=d*Nr;\n",
    "result=Nr/Dr;\n",
    "\n",
    "#Result\n",
    "print \"result is\",result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.32, Page number 4.13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 270.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=137;\n",
    "b=133;\n",
    "\n",
    "#Calculation\n",
    "Nr=(a**3)+(b**3);\n",
    "Dr=(a**2)-(a*b)+(b**2);\n",
    "result=Nr/Dr;\n",
    "\n",
    "#Result\n",
    "print \"result is\",result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.33, Page number 4.14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 2.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=20.25;\n",
    "b=2.8;\n",
    "c=28.35;\n",
    "\n",
    "#Calculation\n",
    "result=a*b/c;\n",
    "\n",
    "#Result\n",
    "print \"result is\",result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.34, Page number 4.14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 0.0247933884298\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=54;\n",
    "b=66;\n",
    "c=33;\n",
    "\n",
    "#Calculation\n",
    "r=a/b;\n",
    "result=r/c;\n",
    "\n",
    "#Result\n",
    "print \"result is\",result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.35, Page number 4.14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 229.0\n",
      "hence middle digit is 2\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=916;\n",
    "b=16;\n",
    "c=4;\n",
    "\n",
    "#Calculation\n",
    "r=a*c/b;\n",
    "\n",
    "#Result\n",
    "print \"result is\",r\n",
    "print \"hence middle digit is 2\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.36, Page number 4.14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 0.00121\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=0.011;\n",
    "b=10;\n",
    "\n",
    "#Calculation\n",
    "x=b*(a**2);\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.37, Page number 4.14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 1000.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=67.6;\n",
    "b=0.26;\n",
    "\n",
    "#Calculation\n",
    "x=a/(b**2);   \n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.38, Page number 4.15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 0.18\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=0.324;\n",
    "b=10;\n",
    "\n",
    "#Calculation\n",
    "x=math.sqrt(a/b);\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.39, Page number 4.15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 2.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=63;\n",
    "b=36;\n",
    "\n",
    "#Calculation\n",
    "r1=(a+b)**2;\n",
    "r2=(a-b)**2;\n",
    "Nr=r1+r2;\n",
    "Dr=(a**2)+(b**2)\n",
    "x=Nr/Dr;\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.40, Page number 4.15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 111.5\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=44.6;\n",
    "b=2.5;\n",
    "\n",
    "#Calculation\n",
    "x=a*b;\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.41, Page number 4.15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 3.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=14;\n",
    "b=46;\n",
    "c=11;\n",
    "d=6;\n",
    "e=4;\n",
    "\n",
    "#Calculation\n",
    "Nr=(a**2)-b;\n",
    "Dr=(c*d)-(e**2);\n",
    "x=Nr/Dr;\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.42, Page number 4.15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 1803\n",
      "answer given in the book varies due to rounding off errors\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=2002;\n",
    "b=10.10;\n",
    "\n",
    "#Calculation\n",
    "x=a-(a/b);\n",
    "\n",
    "#Result\n",
    "print \"result is\",int(x)\n",
    "print \"answer given in the book varies due to rounding off errors\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.43, Page number 4.16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 0.333333333333\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=8;\n",
    "b=3;\n",
    "c=4;\n",
    "d=2;\n",
    "e=6;\n",
    "f=5;\n",
    "g=8;\n",
    "\n",
    "#Calculation\n",
    "Nr=a-(b*c)+d;\n",
    "Dr=-(e*f)+(b*g);\n",
    "x=Nr/Dr;\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.45, Page number 4.16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 4096 or 4 ** 6\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=4;\n",
    "b=3;\n",
    "c=2;\n",
    "d=5;\n",
    "e=0;\n",
    "\n",
    "#Calculation\n",
    "p=(a*b)-(b*c)+(d*e);    #power is calculated using indices\n",
    "x=a**p;\n",
    "y=math.log(x)/math.log(a);\n",
    "\n",
    "#Result\n",
    "print \"result is\",x,\"or\",a,\"**\",int(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.46, Page number 4.16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 1.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=1;\n",
    "b=25/144;\n",
    "c=12;\n",
    "\n",
    "#Calculation\n",
    "r=math.sqrt(a+b);\n",
    "x=(r-a)*c;\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.47, Page number 4.16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 1.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "b=1;\n",
    "a=2;\n",
    "\n",
    "#Calculation\n",
    "x1=a-b;\n",
    "x2=a+b;\n",
    "result=(x1/x2)+(2/3);\n",
    "\n",
    "#Result\n",
    "print \"result is\",result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.48, Page number 4.17"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 28.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=18;\n",
    "b=14;\n",
    "c=84;\n",
    "\n",
    "#Calculation\n",
    "x=(c**2)/(a*b);\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.49, Page number 4.17"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 9.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=243;\n",
    "b=0.8;\n",
    "c=0.4;\n",
    "\n",
    "#Calculation\n",
    "p=b-c;\n",
    "x=a**p;\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.50, Page number 4.17"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 4.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=1.2;\n",
    "b=0.8;\n",
    "\n",
    "#Calculation\n",
    "x=(a**2)+(b**2)+(2*a*b);\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.51, Page number 4.17"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 0.352272727273\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=64/121;\n",
    "b=9/64;\n",
    "c=8/11;\n",
    "d=3/8;\n",
    "\n",
    "#Calculation\n",
    "x=(a-b)/(c+d);\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.52, Page number 4.17"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 1.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=0.1;\n",
    "b=0.75;\n",
    "c=2.5;\n",
    "d=0.05;\n",
    "e=0.125;\n",
    "f=1/4.8;\n",
    "\n",
    "#Calculation\n",
    "r1=(a+b)/(c+d);\n",
    "x=r1/(e+f);\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.53, Page number 4.18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 8731552810114645/18014398509481984\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=1/246;\n",
    "b=2/3;\n",
    "c=1/27;\n",
    "d=4/3;\n",
    "\n",
    "#Calculation\n",
    "r1=a**(-b);\n",
    "r2=c**(-d);\n",
    "x=r1/r2;\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.54, Page number 4.18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 800.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=8;\n",
    "b=5/3;\n",
    "c=125;\n",
    "d=2/3;\n",
    "\n",
    "#Calculation\n",
    "r1=a**b;\n",
    "r2=c**(-d);\n",
    "x=r1/r2;\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.55, Page number 4.18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 1.33333333333\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=6;\n",
    "b=-2;\n",
    "c=81;\n",
    "d=-3/4;\n",
    "\n",
    "#Calculation\n",
    "r1=1/(a**b);\n",
    "r2=c**d;\n",
    "x=r1*r2;\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.56, Page number 4.18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 10.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=math.sqrt(147);\n",
    "b=math.sqrt(27);\n",
    "c=math.sqrt(3);\n",
    "\n",
    "#Calculation\n",
    "x=(a+b)/c;\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.57, Page number 4.19"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 2.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=math.sqrt(98);\n",
    "b=math.sqrt(50);\n",
    "c=math.sqrt(2);\n",
    "\n",
    "#Calculation\n",
    "x=(a-b)/c;\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.58, Page number 4.19"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 2.35\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=math.sqrt(9/25);\n",
    "b=3+(1/16);\n",
    "c=math.sqrt(b);\n",
    "\n",
    "#Calculation\n",
    "x=a+c;\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.59, Page number 4.19"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 0.18\n",
      "answer given in the book is wrong\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=math.sqrt(0.01);\n",
    "b=math.sqrt(0.0064);\n",
    "\n",
    "#Calculation\n",
    "x=a+b;\n",
    "\n",
    "#Result\n",
    "print \"result is\",x\n",
    "print \"answer given in the book is wrong\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.60, Page number 4.19"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 0.688995215311\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=25.6;\n",
    "b=36.1;\n",
    "c=12.1;\n",
    "d=81;\n",
    "e=0.1;\n",
    "\n",
    "#Calculation\n",
    "r1=math.sqrt(a/b);\n",
    "r2=math.sqrt(c/(d*e));\n",
    "x=r1/r2;\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.61, Page number 4.19"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "51 can be expressed as 26 **2 -  25 **2\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "N=51;\n",
    "\n",
    "#Calculation\n",
    "#to express a number as the difference of squares of 2 numbers, we use the formula N=((N+1)/2)**2-((N-1)/2)**2\n",
    "a=(N+1)/2;\n",
    "b=(N-1)/2;\n",
    "#N can be expressed as (a**2)-(b**2)\n",
    "\n",
    "#Result\n",
    "print \"51 can be expressed as\",int(a),\"**2 - \",int(b),\"**2\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.62, Page number 4.19"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 308.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=7;\n",
    "b=11;\n",
    "c=1232;\n",
    "\n",
    "#Calculation\n",
    "x2=a*b*c;\n",
    "x=math.sqrt(x2);\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.63, Page number 4.20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 5.41666666667\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=3+(1/4);\n",
    "b=4+(1/3);\n",
    "\n",
    "#Calculation\n",
    "Nr=(a**4)-(b**4);\n",
    "Dr=(a**2)-(b**2);\n",
    "result=math.sqrt(Nr/Dr);\n",
    "\n",
    "#Result\n",
    "print \"result is\",result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.64, Page number 4.20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total score in innings is 162.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=2/9;\n",
    "b=8;\n",
    "\n",
    "#Calculation\n",
    "x=b/(a**2);    #total score in innings\n",
    "\n",
    "#Result\n",
    "print \"total score in innings is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.65, Page number 4.20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 17.125\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=64;\n",
    "b=32;\n",
    "c=-1/2;\n",
    "d=4/5;\n",
    "\n",
    "#Calculation\n",
    "r1=(1/a)**0;\n",
    "r2=a**c;\n",
    "r3=b**d;\n",
    "result=r1+r2+r3;\n",
    "\n",
    "#Result\n",
    "print \"result is\",result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.66, Page number 4.21"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 3.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=243;\n",
    "b=0.12;\n",
    "c=0.08;\n",
    "\n",
    "#Calculation\n",
    "p=b+c;\n",
    "result=a**p;\n",
    "\n",
    "#Result\n",
    "print \"result is\",result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.67, Page number 4.21"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 12.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=2;\n",
    "b=64;\n",
    "\n",
    "#Calculation\n",
    "c=math.log(b)/math.log(a);\n",
    "n=c*a;\n",
    "\n",
    "#Result\n",
    "print \"result is\",n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.68, Page number 4.21"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 36.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=1/216;\n",
    "b=2/3;\n",
    "\n",
    "#Calculation\n",
    "x=1/(a**b);\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.69, Page number 4.21"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 16.0\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=-2;\n",
    "\n",
    "#Calculation\n",
    "b=a**a;\n",
    "x=b**a;\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.70, Page number 4.21"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 2.4\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=11+(1/3);\n",
    "b=4+(8/10);\n",
    "c=22+(2/3);\n",
    "\n",
    "#Calculation\n",
    "x=a*b/c;\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.71, Page number 4.22"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 1.0404\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "a=1.06;\n",
    "b=0.04;\n",
    "c=4;\n",
    "\n",
    "#Calculation\n",
    "r1=(a+b)**2;\n",
    "x=r1-(4*a*b);\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.72, Page number 4.22"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is +/- 1/2\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "from fractions import Fraction\n",
    "\n",
    "#Variable declaration\n",
    "a2plusb2=45;\n",
    "ab=18;\n",
    "\n",
    "#Calculation\n",
    "Nr=math.sqrt(a2plusb2+(2*ab));\n",
    "result=Nr/ab;\n",
    "\n",
    "#Result\n",
    "print \"result is +/-\",Fraction(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example number 4.75, Page number 4.23"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "result is 4\n"
     ]
    }
   ],
   "source": [
    "#importing modules\n",
    "import math\n",
    "from __future__ import division\n",
    "\n",
    "#Variable declaration\n",
    "#by comparing the equations we get\n",
    "rootx=2;\n",
    "\n",
    "#Calculation\n",
    "x=rootx**2;\n",
    "\n",
    "#Result\n",
    "print \"result is\",x"
   ]
  }
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