Question

Java Program Create a Project called “SquareRoot” with a class called “SquareRoot”.

Write a Java program to compute the square root of a double using the algorithm

The ancient Babylonians had an algorithm for determining the square root of a number a. Start with an initial guess of a / 2. Then find the average of your guess g and a / g. That’s your next guess. Repeat until two consecutive guesses are close enough.

For example,

Square Root by Tai Babylonia

Enter the target value: 1000

Enter the initial guess: 30

31.666666667 squared equals 1002.7777778, which is 100.27777778% of the target.

31.622807018 squared equals 1000.0019237, which is 100.00019237% of the target.

31.622776602 squared equals 1000.0000000, which is 100.00000000% of the target.

The calculated square root of 1000.0000000 is 31.622776602.

To format the numbers, use the format specifier %.11g – this will always show 11 significant figures and will allow very small numbers to be displayed correctly as well:

Square Root by Tai Babylonia

Enter the target value: 0.00000045678

Enter the initial guess: .005

0.0025456780000 squared equals 6.4804764797e-06, which is 1418.7303471% of the target.

0.0013625557670 squared equals 1.8565582182e-06, which is 406.44472573% of the target.

0.00084889671095 squared equals 7.2062562587e-07, which is 157.76207931% of the target.

0.00069349168790 squared equals 4.8093072119e-07, which is 105.28716695% of the target.

0.00067607927935 squared equals 4.5708319197e-07, which is 100.06637593% of the target.

0.00067585505123 squared equals 4.5678005028e-07, which is 100.00001101% of the target.

0.00067585501404 squared equals 4.5678000000e-07, which is 100.00000000% of the target.

The calculated square root of 4.5678000000e-07 is 0.00067585501404.

To create the loop, we will use the following construct:

while (true) {
// compute next guess

// termination condition

if ( /* guess is close enough */ ) break;

}

After you compute the percentage, consider the guess to be close enough if the absolute value of the percentage minus 100 is less than 1E-8.

Answer 1

import java.util.Scanner;

public class SqrtTest {

        public static void main(String[] args) {
                
                Scanner in = new Scanner(System.in);
                
                System.out.println("Square Root by Tai Babylonia");
                System.out.println("Enter the target value: ");
                
                double target = in.nextDouble();
                
                System.out.println("Enter the initial guess: ");
                double initialGuess = in.nextDouble();
                
                double currentGuess = initialGuess, prevGuess;
                
                do {
                        prevGuess = currentGuess;
                        currentGuess = (prevGuess + target/prevGuess)/2.0;
                        
                        double value = currentGuess * currentGuess;
                        double percChange = value * 100 / target;
                        System.out.printf("%.11g squared equals %.11g, "
                                        + "which is %.11g%% of the target\n",
                                        currentGuess, value, percChange);
                        
                } while(Math.abs(currentGuess - prevGuess) > Math.pow(10, -8));
                
                
                System.out.printf("The calculated square root of %.11g is %.11g.\n"
                                , target, currentGuess);
                in.close();
                
        }

}

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