Let’s say you are given a number, a, and you want to find its square root. One way to do that is to start with a very rough guess about the answer, x0, and then improve the guess using the following formula: x1 = (x0 + a/x0)/2 For example, if we want to find the square root of 9, and we start with x0 = 6, then x1 = (6 + 9/6)/2 = 15/4 = 3.75, which is closer. We can repeat the procedure, using x1 to calculate x2, and so on. In this case, x2 = 3.075 and x3 = 3.00091. So that is converging very quickly on the right answer(which is 3). Write a method called squareRoot that takes a double as a parameter and that returns an approximation of the square root of the parameter, using this technique. You may not use Math. sqrt. In java

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Explanation:

package com.squarerrot;

public class SquareRoot {

/**

*

*/

public static double squareRoot(double input) {

System.out.println("Trace for input:" + input);

//random value initialized to 6 here

double output, guessValue = 6, previousValue = 0;

while (input - (output = approximateValue(input, guessValue)) >= 0.00005

&& previousValue != output) {

guessValue = output;

previousValue = output;

System.out.println(output);

}

return output;

}// end of method squareRoot

// calculate the approximate value

public static double approximateValue(double input, double start) {

return (start + (input / start)) / 2;

}// end of method approximateValue

// test the square root method

public static void main(String[] args) {

System.out.println("Square Root of 9:" + squareRoot(9));

System.out.println("Square Root of 16:" + squareRoot(16));

}// end of method main

}// end of the class