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Authors:
Walter Savitch ,kenrick Mock
Chapter:
Console Input And Output
Exercise:
Programming Projects
Question:1 | ISBN:9780132830317 | Edition: 5

Question

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 five times, and outputs the answer as a double to two decimal places. Your answer will be most accurate for small values of n.


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Answer

Program:

// BabylonianDemo.java
import java.util.Scanner;
public class BabylonianDemo 
{
	public static void main(String[] args) 
	{
		Scanner keyboard = new Scanner(System.in);
		
		double n;
		double guess;
		double r;
		
		System.out.print("Enter a value for n: ");
		n = keyboard.nextDouble();
		
		guess = n / 2;
		
		r = n / guess;			
		guess = (guess + r) / 2.0;
		
		r = n / guess;			
		guess = (guess + r) / 2.0;
		
		r = n / guess;			
		guess = (guess + r) / 2.0;
		
		r = n / guess;			
		guess = (guess + r) / 2.0;
		
		r = n / guess;			
		guess = (guess + r) / 2.0;
		
		System.out.printf(
			"The square root of %.2f is approximately: %.2f\n", n, guess);
	}
}

Output:

Enter a value for n: 16
The square root of 16.00 is approximately: 4.00

 

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Discussions

sinaaa

import java.util.Scanner;
public class BabylonianAlgorithm {

    public static void main(String[] args) {
        Scanner keyboard = new Scanner(System.in);
        
        System.out.println("Enter a positive number: ");
        int n = keyboard.nextInt();
        System.out.println("Enter number of iteration: ");
        int iterations = keyboard.nextInt();
        
        double guess = (n / 2);
        for (int i = 1; i <= iterations; i++) {
        double r = (n / guess);
        guess = (guess + r) / 2;
        
        }
        System.out.printf("The square of %,d is: %,.7f", n, guess);
        
        keyboard.close();
    }

}
 

Post the discussion to improve the above solution.