Babylonian method for square root

Algorithm:
This method can be derived from (but predates) Newton–Raphson method.


1 Start with an arbitrary positive start value x (the closer to the 
   root, the better).
2 Initialize y = 1.
3. Do following until desired approximation is achieved.
  a) Get the next approximation for root using average of x and y
  b) Set y = n/x

Implementation:

/*Returns the square root of n. Note that the function */
float squareRoot(float n)
{
  /*We are using n itself as initial approximation
   This can definitely be improved */
  float x = n;
  float y = 1;
  float e = 0.000001; /* e decides the accuracy level*/
  while(x - y > e)
  {
    x = (x + y)/2;
    y = n/x;
  }
  return x;
}
/* Driver program to test above function*/
int main()
{
  int n = 50;
  printf ("Square root of %d is %f", n, squareRoot(n));
  getchar();
}

Example:

n = 4 /*n itself is used for initial approximation*/
Initialize x = 4, y = 1
Next Approximation x = (x + y)/2 (= 2.500000), 
y = n/x  (=1.600000)
Next Approximation x = 2.050000,
y = 1.951220
Next Approximation x = 2.000610,
y = 1.999390
Next Approximation x = 2.000000, 
y = 2.000000
Terminate as (x - y) > e now.

If we are sure that n is a perfect square, then we can use following method. The method can go in infinite loop for non-perfect-square numbers. For example, for 3 the below while loop will never terminate.

/*Returns the square root of n. Note that the function
  will not work for numbers which are not perfect squares*/
unsigned int squareRoot(int n)
{
  int x = n;
  int y = 1;
  while(x > y)
  {
    x = (x + y)/2;
    y = n/x;
  }
  return x;
}
/* Driver program to test above function*/
int main()
{
  int n = 49;
  printf (" root of %d is %d", n, squareRoot(n));
  getchar();
}

 

 

Disclaimer: This does not belong to TechCodeBit, its an article taken from the below
source and credits.
source and credits:http://www.geeksforgeeks.org/square-root-of-a-perfect-square/
We have built the accelerating growth-oriented website for budding engineers and aspiring job holders of technology companies such as Google, Facebook, and Amazon
If you would like to study our free courses you can join us at

http://www.techcodebit.com. #techcodebit #google #microsoft #facebook #interview portal #jobplacements
#technicalguide

rakesh

Leave a Reply

Your email address will not be published. Required fields are marked *

Skip to toolbar