Java/src/main/java/com/thealgorithms/maths/SquareRootWithNewtonRaphsonMethod.java

package com.thealgorithms.maths;

import java.util.Scanner;

/*
*To learn about the method, visit the link below :
* https://en.wikipedia.org/wiki/Newton%27s_method
*
* To obtain the square root, no built-in functions should be used
*
* The formula to calculate the root is : root = 0.5(x + n/x),
* here, n is the no. whose square root has to be calculated and
* x has to be guessed such that, the calculation should result into
* the square root of n.
* And the root will be obtained when the error < 0.5 or the precision value can also
* be changed according to the user preference.
*/

public class SquareRootWithNewtonRaphsonMethod {

    public static double squareRoot (int n) {

        double x = n;                         //initially taking a guess that x = n.
        double root = 0.5 * (x + n/x);        //applying Newton-Raphson Method.

        while (Math.abs(root - x) > 0.0000001) {      //root - x = error and error < 0.0000001, 0.0000001 is the precision value taken over here.

            x = root;                         //decreasing the value of x to root, i.e. decreasing the guess.
            root = 0.5 * (x + n/x);
        }

        return root;
    }
}