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Finding Square Root without using sqrt()

This code shows how to find out the square root of a number without using the sqrt() function. The result obtained by both functions are the same and hence can also be used as an alternative sqrt() function.

Submitted By: born2c0de
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Views: 20,445

Language: C++
Last Modified: August 20, 2005

Snippet


  1. /*          Code written by Sanchit Karve
  2.                   A.K.A born2c0de
  3.                   Contact Me at born2c0de AT hotmail.com
  5.                   20 August, 2005
  7. */
  8.  
  9.  
  10.  
  11.  
  12. #include <iostream>
  13. #include <math.h>
  14.  
  15. using namespace std;
  16.  
  17.  
  18. float sqroot(float m)
  19. {
  20.      float i=0;
  21.    float x1,x2;
  22.    while( (i*i) <= m )
  23.           i+=0.1;
  24.    x1=i;
  25.    for(int j=0;j<10;j++)
  26.    {
  27.         x2=m;
  28.       x2/=x1;
  29.       x2+=x1;
  30.       x2/=2;
  31.       x1=x2;
  32.    }
  33.    return x2;
  34. }
  35.  
  36. int main()
  37. {
  38.    cout<<"Enter a Number:";
  39.    int no;
  40.    cin>>no;
  41.      cout<<"Square Root using sqroot()= "<<sqroot(no)<<endl
  42.        <<"Square Root using sqrt()  = "<<sqrt(no);
  43.  
  44.    return 0;
  45. }
  46.  

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Comments


bodom658 2008-03-05 20:21:48

very cool! thanks for sharing!
mikeblas 2008-04-20 13:25:58

I suppose this method kind of works, but, WOW, is it slow! You start at 0, then multiply 0*0 to find that it's less than m. Then, you add 0.1, multiplying that times itself -- you get 0.01, and it's still less than m. You keep adding 0.1 to your candidate root until it's greater than m when squared... then use that as your starting point for ten iterations of approximation. What if m is 750,000,000 ? It will take you more than 270,000 multiplications to find the answer.

born2c0de 2008-04-21 04:23:44

Yes, it will. It uses a method of approximations and has that limitation. All approximation algorithms have that property, including Newton Raphson's, Runge Kutta's etc.

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