#include <stdio.h>
double squareRoot(double N) {
if (N < 0) {
printf("Negative numbers do not have real square roots.\n");
return -1; // Indicate an error for negative input
}
double guess = N; // Start with the number itself as the initial guess
double epsilon = 0.00001; // Define the accuracy level
double newGuess;
// Repeat until the guess is close enough to the actual square root
do {
newGuess = (guess + N / guess) / 2; // Update guess using the formula
// Check if the difference is within the acceptable range
if (newGuess - guess < epsilon && newGuess - guess > -epsilon) {
break; // If close enough, break the loop
}
guess = newGuess; // Update the guess
} while (1);
return newGuess; // Return the approximated square root
}
int main() {
double number;
printf("Enter a number to find its square root: ");
scanf("%lf", &number); // Take user input
double result = squareRoot(number); // Call the function
if (result != -1) { // Check for negative input
printf("The square root of %.2lf is approximately %.5lf\n", number, result);
}
return 0;
}
Explanation:
The program uses the Newton-Raphson method, an iterative technique to estimate the square root of a number.
Key Components
- Function
squareRoot(double x):- Starts with an initial guess (
g = x / 2). - Iteratively improves the guess using the formula: g=g+xg2g = \frac{g + \frac{x}{g}}{2}g=2g+gx
- Continues until the guess is sufficiently close to the actual square root (within a small threshold,
epsilon).
- Starts with an initial guess (
- Main Function:
- Prompts the user for a number.
- Checks if the number is negative (since square roots of negatives are not real).
- Calls the
squareRootfunction and displays the result
Output:
1.Enter a number to find its square root: -9
Cannot compute square root of a negative number.
2. Enter a number to find its square root: 36
The square root of 36.00 is approximately 6.00000
3. Enter a number to find its square root: 50
The square root of 50.00 is approximately 7.07107