Add Newton Raphson method (#3224)

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

@@ -0,0 +1,34 @@
+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;
+    }
+}