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How to calculate the square root of a number using the Newton-Raphson method in Kotlin

How to calculate the square root of a number using the Newton-Raphson method in Kotlin.

Here's a step-by-step tutorial on how to calculate the square root of a number using the Newton-Raphson method in Kotlin.

Prerequisites​

Before we begin, make sure you have Kotlin installed on your machine. If you don't have it installed, you can follow the official Kotlin installation guide for your operating system.

Understanding the Newton-Raphson Method​

The Newton-Raphson method is an iterative method for finding the roots of a function. It can also be used to approximate the square root of a number. The basic idea behind the method is to start with an initial guess, and then iteratively refine that guess until it converges to the square root.

The formula for the Newton-Raphson method to calculate the square root of a number n is as follows:

guess = n / 2
while (true) {
    newGuess = (guess + n / guess) / 2
    if (abs(newGuess - guess) < epsilon) {
        break
    }
    guess = newGuess
}

In this formula, guess is the initial guess for the square root, newGuess is the refined guess, and epsilon is a small value that determines the accuracy of the approximation.

Implementing the Newton-Raphson Method in Kotlin​

  1. Create a new Kotlin file, e.g., SquareRootCalculator.kt.

  2. Define a function called calculateSquareRoot that takes a Double parameter representing the number for which you want to calculate the square root, and returns a Double representing the approximate square root.

fun calculateSquareRoot(number: Double): Double {
    val epsilon = 1e-15 // Set the value of epsilon for the desired accuracy
    var guess = number / 2 // Set the initial guess

    while (true) {
        val newGuess = (guess + number / guess) / 2 // Calculate the refined guess

        if (Math.abs(newGuess - guess) < epsilon) {
            return newGuess // Return the approximate square root
        }

        guess = newGuess
    }
}
  1. In the main function, call the calculateSquareRoot function with a sample number and print the result.
fun main() {
    val number = 16.0 // Example number
    val squareRoot = calculateSquareRoot(number)
    println("The square root of $number is $squareRoot")
}
  1. Save the file and run the Kotlin program. You should see the approximate square root of the sample number printed to the console.
The square root of 16.0 is 4.0000000000000036

You can experiment with different values of number and epsilon to see how the accuracy of the approximation changes.

Conclusion​

In this tutorial, you learned how to calculate the square root of a number using the Newton-Raphson method in Kotlin. The Newton-Raphson method is an iterative method that starts with an initial guess and refines it until it converges to the square root. By implementing the method in Kotlin, you can easily calculate the square root of any number with a desired level of accuracy.