# Babylonian method to find square root in C++

Today we will learn the Babylonian method to find the square root using C++.

This method basically originates from the newton-raphson method.

We all know what a square root of a number is and this method is an olden time approach to computing just that.

The method basically follows the below algorithm –

- First, we start off with a random positive value as close to the root as possible
- then we initialize a variable say y=1;
- Then follow the below two steps until when are left with the answer

- find the avg of x & y and get the approx for the root
- and we set y= n/x

If we follow the above steps in a loop we will ultimately end up the square root of the number itself while using the Babylonian method to solve it :

## Babylonian method to find square root in C++

Below defined is the function that computes the square root number the number itself as the input –

#include<iostream.h> #include<math.h> #include<stdio.h> using namespace std; int main() { float sqroot(float a) { //right now we start the approximation with a itself float x = a; float y = 1; //value of e should be accurate float e = 0.000001; while (x - y > e) { x = (x + y) / 2; y = a / x; } return x; } int no; cout<<"Enter number to find square root of"; cin>>no; cout<<"Square root using babylonian method is "<<sqroot(no); return 0; }

OUTPUT - Square root using babylonian method is 8.366600

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