C Program to Find Square Root of a Number

This C program calculates the square root of a given number using the Newton-Raphson method. The Newton-Raphson method is an iterative numerical technique for finding approximations of the roots (in this case, square roots) of a real-valued function.

The square root of a number is a mathematical operation that determines a value which, when multiplied by itself, gives the original number. In programming, finding the square root of a number is a common task that can be accomplished using various algorithms.

Program Statement

Write a C program that calculates the square root of a given number using the Newton-Raphson method. The program should prompt the user to enter a non-negative number and validate the input. It should then calculate the square root with a specified level of precision and display the result.

C Program to Find Square Root of a Number

#include <stdio.h>

double squareRoot(double num) {
    double epsilon = 0.00001;  // Desired precision
    double guess = num;       // Initial guess

    while ((guess * guess - num) > epsilon) {
        guess = (guess + num / guess) / 2.0;
    }

    return guess;
}

int main() {
    double number;
    printf("Enter a number: ");
    scanf("%lf", &number);

    double result = squareRoot(number);
    printf("Square root of %.2lf is %.4lf\n", number, result);

    return 0;
}

How it works

1. The program begins by displaying a prompt asking the user to enter a number.
2. The input number is read from the user using the scanf function and stored in the variable number.
3. The program then validates whether the input number is non-negative. If the number is negative, it displays an error message stating that the square root of a negative number is not defined. The program terminates at this point.
4. If the input number is non-negative, the program proceeds to the squareRoot function. This function takes the input number as a parameter and calculates its square root using the Newton-Raphson method.
5. Inside the squareRoot function, two variables, x and y, are initialized with the input number and 1, respectively. The variable epsilon is set to a small value, such as 0.000001, to determine the desired precision of the square root calculation.
6. The function enters a while loop that continues until the difference between x and y is less than the epsilon value. This ensures that the desired precision is achieved.
7. In each iteration of the loop, x is updated as the average of x and y, and y is updated as the input number divided by x. These steps are based on the Newton-Raphson method, which iteratively refines the guess for the square root.
8. Once the loop exits, the final value of x represents the calculated square root of the input number. The function returns this value.
9. Back in the main function, the calculated square root is stored in the variable result.
10. The program then displays the calculated square root with a specified precision using the printf function.
11. Finally, the program terminates, and the execution completes.

The Newton-Raphson method provides a good approximation for the square root of a number, and by iterating the steps, the algorithm refines the guess until the desired precision is achieved.

Input/Output