Babylonian method to find the square root

Babylonian method to find the square root is based on Newton–Raphson method.

We start form y=1 and x = number and then we find approximate root by finding average x and y. With each iteration, we update value of y = number / x.

Algorithm

Begin
   x := number
   y := 1
   precision := 0.001
   while error > precision, do
      x := (x+y) / 2
      y := number / x
   done
   return x
End

Implementation

#include<bits/stdc++.h>
using namespace std;

float bbln_sqrt(float number) {
   float x = number, y = 1;              // let's say sqrt of number is 1
   float precision = 0.001;           // Considering precision of 0.001

   while(abs(x - y)/abs(x) > precision) {
      x = (x + y)/2;
      y = number/x;
   }
   return x;
}

int main() {
   int n;
   cout << "Enter Number ";
   cin >> n;
   cout << "SQRT of " << n <<" is: " << bbln_sqrt(n);
}

Enter Number 78
SQRT of 78 is: 8.83177