C++ Program to Find Square Root of a Number

You can find the square root in C++ using the sqrt() function from the cmath library like this: double root = sqrt(number);.

Examples

Input16

OutputSquare root of 16 is 4

Input25

OutputSquare root of 25 is 5

Input0

OutputSquare root of 0 is 0

How to Think About It

To find the square root of a number, you first get the number from the user. Then use the built-in sqrt() function which calculates the square root. Finally, print the result. This approach is simple and uses the standard math library.

Algorithm

1

Get the input number from the user.

2

Use the <code>sqrt()</code> function to calculate the square root.

3

Display the result to the user.

Code

cpp

#include <iostream>
#include <cmath>

int main() {
    double number;
    std::cout << "Enter a number: ";
    std::cin >> number;
    double root = sqrt(number);
    std::cout << "Square root of " << number << " is " << root << std::endl;
    return 0;
}

Output

Enter a number: 16
Square root of 16 is 4

Dry Run

Let's trace the input 16 through the code

1

Input

User enters 16, so number = 16

2

Calculate square root

root = sqrt(16) which equals 4

3

Output

Prints: Square root of 16 is 4

number	root
16	4

Why This Works

Step 1: Include cmath library

The cmath library provides the sqrt() function to calculate square roots.

Step 2: Read input

We get the number from the user using std::cin.

Step 3: Calculate and print

We call sqrt(number) to get the square root and print it with std::cout.

Alternative Approaches

Using pow() function

cpp

#include <iostream>
#include <cmath>

int main() {
    double number;
    std::cout << "Enter a number: ";
    std::cin >> number;
    double root = pow(number, 0.5);
    std::cout << "Square root of " << number << " is " << root << std::endl;
    return 0;
}

Uses <code>pow()</code> with exponent 0.5 instead of <code>sqrt()</code>; slightly less direct but works the same.

Manual approximation (Newton's method)

cpp

#include <iostream>

int main() {
    double number, guess, epsilon = 0.00001;
    std::cout << "Enter a number: ";
    std::cin >> number;
    guess = number / 2;
    while ((guess * guess - number) > epsilon || (number - guess * guess) > epsilon) {
        guess = (guess + number / guess) / 2;
    }
    std::cout << "Square root of " << number << " is " << guess << std::endl;
    return 0;
}

Calculates square root manually using Newton's method; useful if math library is unavailable but more complex.

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

Time Complexity

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

Space Complexity

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

Which Approach is Fastest?

Using sqrt() is fastest and simplest; manual methods are slower and more complex.

Approach	Time	Space	Best For
sqrt() function	O(1)	O(1)	Simple and fast calculation
pow() function	O(1)	O(1)	When exponentiation is needed
Newton's method	O(log n)	O(1)	Learning algorithm or no math library