Exploring the Square Root Function in Java: An In-Depth Guide

When it comes to programming, Java is a popular programming language known for its reliability, stability, and security features. If you are a Java programmer, you know that calculations are an essential part of programming, and one of the essential calculations is finding the square root of a number.

This article will explore two different ways of finding the square root of a number in Java. The first method involves using the built-in sqrt() method, and the second method involves using the Math.pow() method and a custom formula.

We will start with an overview of the sqrt() method and then move on to the second method.

## Using the sqrt() Method to Find the Square Root of a Number in Java

The sqrt() method is a built-in method of the Java Math class that returns the square root of a given number. The method takes a double type argument and returns a double type result.

Here’s an example code to demonstrate how to use the sqrt() method to find the square root of a number in Java:

“`java

double number = 25;

double squareRoot = Math.sqrt(number);

System.out.println(“The square root of ” + number + ” is ” + squareRoot);

“`

In this example, the declaration of the variable ‘number’ assigns a value of 25. The sqrt() method is then called with the ‘number’ variable as the argument.

The resulting square root of ’25’ is stored in the ‘squareRoot’ variable. Finally, the value of the ‘squareRoot’ variable is printed to the console.

It is essential to note that the sqrt() method returns NaN (not a number) if the input argument is negative. For example, calling sqrt(-1) results in a NaN value.

“`java

double negativeNumber = -5;

double negativeSquareRoot = Math.sqrt(negativeNumber);

System.out.println(negativeSquareRoot); // Output: NaN

“`

## Finding the Square Root of a Number Without Using sqrt() Method in Java

The second method of finding the square root of a number in Java involves using the Math.pow() method and a custom formula. The Math.pow() method returns the base to the power of the exponent.

This method can be used to calculate any power, including the square root of a number. To find the square root of a number, you can raise the number to the power of 1/2.

An alternative formula to calculate the square root of a number that does not involve using a built-in method is:

“`java

double number = 25;

double guess = number;

double tolerance = 1e-15;

while(Math.abs(guess – number/guess) > tolerance*guess) {

guess = (number/guess + guess) / 2.0;

}

System.out.println(“The square root of ” + number + ” is ” + guess);

“`

In this example, we begin by initializing the starting guess for the square root as ‘number’. We use the tolerance of 1e-15, which represents the maximum allowable difference between the current guess and the actual square root.

We then use a while loop to iteratively improve the current guess. The loop condition is satisfied when the absolute difference between the current guess and the calculated value of the square root is smaller than the tolerance times guess.

The formula used to update the guess at each iteration is (number/guess + guess) / 2.0. This formula is known as the Babylonian method or the Newton-Raphson method and is based on the idea that the average of the current guess and the actual root provides a better estimate than the guess itself. It is essential to note that the custom formula method described can result in Double.POSITIVE_INFINITY or Double.NaN for some input values.

For example, calling the formula method with a negative input value results in Double.NaN.

“`java

double negativeNumber = -5;

double customFormulaSquareRoot = customFormula(negativeNumber);

System.out.println(customFormulaSquareRoot); // Output: NaN

“`

## Conclusion

In conclusion, finding the square root of a number is an essential computation in programming, and Java provides two built-in methods to calculate the square root and a custom formula as an alternative. By using the sqrt() method, you can quickly find the square root of any real number and receive NaN for negative input values.

On the other hand, using the custom formula allows for more control and can handle negative input values with the downside of being a more complex solution. We hope that this guide has provided you with valuable information on how to calculate the square root of a number in Java.

By mastering these concepts, you’ll be empowered to write robust code that can handle even the most complex calculations. In conclusion, this article explores two methods of finding the square root of a number in Java.

The built-in sqrt() method is easy to use and quickly calculates the square root of a number but returns NaN for negative input values. The custom formula method requires more coding but can handle negative input values.

The Math.pow() method and the custom formula enable Java programmers to calculate square roots and make programming more effective. It is essential to choose the method that best suits your needs as a programmer and the requirements of your specific project.