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; } }