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 void main(String[] args) {
        Scanner sc =new Scanner(System.in);
        System.out.println("enter the number");
        int a = sc.nextInt();
        System.out.println(squareRoot(a));
        sc.close();
    }

    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;
    }
}