# 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
```