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.