package newton_sqrt;

import java.util.Scanner;

public class Newton_sqrt {

    public static void main(String[]args) {

        Scanner scan = new Scanner(System.in);

        System.out.println("Newton's Method for Square Roots");

        System.out.println("Please enter a number greater than zero:");
        double alpha = scan.nextDouble();

        double beta = alpha;
        double gamma = 1;

        while(Math.abs(beta-gamma)>.000001) {
            gamma = beta;
            beta = (0.5*((alpha/beta)+beta));
        }

        System.out.println("Newton says: " + beta);

        double delta= Math.sqrt(Math.abs(alpha));

        System.out.println("Math says: " + delta);
        scan.close();
    }
}