Question

Chapter 3 Exercise 1
Babylonian Algorithm. The Babylonian algorithm to compute the square root of a positive number n is as follows:

      1. Make a guess at the answer (you can pick n/2 as your initial guess).
      2. Computer = n / guess.
      3. Set guess = (guess +r) / 2.
      4. Go back to step 2 until the last two guess values are within 1% of each other.

Write a program that inputs an integer for n, iterates through the Babylonian algorithm until the guess is within 1% of the previous guess, and outputs the answer as a doubleto two decimal places. Your answer should be accurate even for large values of n.

INPUT and PROMPTS. The program prints "This program estimates square roots." and then prompts for a positive integer as follows: ("Enter an integer to estimate the square root of: " and then reads in the integer.

OUTPUT. Each time a new guess is computed, the program prints ithe line "Current guess: g", where g is the current guess, printed out with no special formatting. The final output is "The estimated square root of x is y", where x is the integer that was read in and y is the value computed by the procedure described above, printed out to two decimal places and a toal of six characters.

CLASS NAMES. Your program class should be called Babylonia

Answer 1

Answer:

import java.util.Scanner;

public class BabylonianAlgorithm
{  
   /*The Babylonian algorithm to compute the square root of a positive number n is as
   follows:
   1. Make a guess at the answer (you can pick n /2 as your initial guess).
   2. Compute r = n / guess
   3. Set guess = (guess +r)/ 2
   4. Go back to step 2 for as many iterations as necessary. The more you repeat steps
       2 and 3, the closer guess will become to the square root of n .
   Write a program that inputs a double for n , iterates through the Babylonian algorithm
   ten times, and outputs the answer as a double to two decimal places. Your
   answer will be most accurate for small values of n.
   */
   public static void main(String[] args)
   {
       Scanner input = new Scanner(System.in);
       Double n, r, guess;
      
       System.out.println("Please enter a positive number to compute it's square root.");
       n = input.nextDouble();
      
       //initial guess n/2
       guess = n / 2;
      
       for(int i = 0; i < 10; i++)
       {
           r = n / guess;
           guess = (guess + r) / 2;
       }
      
       System.out.print("The guess for the the square root of " + n);
       System.out.printf(" is %.2f.%n", n, guess);
      
       input.close();
   }
}