# 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 –

1. First, we start off with a random positive value as close to the root as possible
2. then we initialize a variable say y=1;
3. 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

```