C# Program to Find the Cube Root of a Number

using System;

namespace CubeRootCalculator
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.WriteLine("Cube Root Calculator");
            Console.WriteLine("====================");
            Console.WriteLine("This program calculates the cube root of a number.");

            // Input
            Console.Write("Enter a number: ");
            double inputNumber;
            if (double.TryParse(Console.ReadLine(), out inputNumber))
            {
                // Calculate cube root
                double cubeRoot = CalculateCubeRoot(inputNumber);

                // Output
                Console.WriteLine($"The cube root of {inputNumber} is approximately {cubeRoot:F6}");
            }
            else
            {
                Console.WriteLine("Invalid input. Please enter a valid number.");
            }
        }

        // Function to calculate cube root using Newton-Raphson method
        static double CalculateCubeRoot(double number)
        {
            double guess = number / 3.0; // Initial guess
            double tolerance = 1e-6;    // Tolerance for approximation

            while (Math.Abs(guess * guess * guess - number) > tolerance)
            {
                guess = (2.0 * guess + number / (guess * guess)) / 3.0; // Newton-Raphson formula
            }

            return guess;
        }
    }
}