C Program to Find Square Root of a Number

You can find the square root in C using sqrt() function from math.h library like this: double root = sqrt(number); where number is the input value.

Examples

Input16

OutputSquare root of 16 is 4.000000

Input25

OutputSquare root of 25 is 5.000000

Input0

OutputSquare root of 0 is 0.000000

How to Think About It

To find the square root of a number, first get the number from the user. Then use the built-in sqrt() function which calculates the square root. Finally, print the result. This avoids manual calculation and uses reliable library code.

Algorithm

1

Get the input number from the user.

2

Include the math library to use the sqrt function.

3

Call the sqrt function with the input number.

4

Store the result in a variable.

5

Print the square root result.

Code

c

#include <stdio.h>
#include <math.h>

int main() {
    double number, root;
    printf("Enter a number: ");
    scanf("%lf", &number);
    root = sqrt(number);
    printf("Square root of %.2lf is %.6lf\n", number, root);
    return 0;
}

Output

Enter a number: 16
Square root of 16.00 is 4.000000

Dry Run

Let's trace input 16 through the code

1

Input number

User enters 16, stored in variable number = 16

2

Calculate square root

Call sqrt(16), which returns 4.0, stored in root

3

Print result

Print 'Square root of 16.00 is 4.000000'

Step	Variable	Value
1	number	16
2	root	4.0
3	output	Square root of 16.00 is 4.000000

Why This Works

Step 1: Include math library

The math.h library provides the sqrt() function to calculate square roots accurately.

Step 2: Use sqrt function

Calling sqrt(number) returns the square root of the input number as a double.

Step 3: Print the result

The program prints the original number and its square root formatted to two decimal places.

Alternative Approaches

Manual approximation using Newton's method

c

#include <stdio.h>

int main() {
    double number, root, guess;
    printf("Enter a number: ");
    scanf("%lf", &number);
    guess = number / 2.0;
    for (int i = 0; i < 10; i++) {
        guess = (guess + number / guess) / 2.0;
    }
    printf("Approximate square root of %.2lf is %lf\n", number, guess);
    return 0;
}

This method approximates the square root without math library but requires iteration and may be less precise.

Using pow function

c

#include <stdio.h>
#include <math.h>

int main() {
    double number, root;
    printf("Enter a number: ");
    scanf("%lf", &number);
    root = pow(number, 0.5);
    printf("Square root of %.2lf is %lf\n", number, root);
    return 0;
}

Using <code>pow()</code> with exponent 0.5 also calculates square root but is less direct than <code>sqrt()</code>.

Complexity: O(1) time, O(1) space

Time Complexity

The sqrt() function runs in constant time as it uses hardware or optimized library calls.

Space Complexity

Only a few variables are used, so space complexity is constant.

Which Approach is Fastest?

Using sqrt() is fastest and most accurate; manual methods are slower and less precise.

Approach	Time	Space	Best For
sqrt() function	O(1)	O(1)	Fast and accurate calculation
Newton's method	O(n) with iterations	O(1)	Learning algorithm and approximation
pow() function	O(1)	O(1)	General power calculations including roots