C# Program to Find Square Root of a Number

In C#, you can find the square root of a number using Math.Sqrt(number). For example, double result = Math.Sqrt(16); will give you 4.

Examples

Input16

Output4

Input25

Output5

Input0

Output0

How to Think About It

To find the square root of a number, think of it as finding a value that when multiplied by itself gives the original number. We use the built-in Math.Sqrt function in C# which does this calculation for us easily.

Algorithm

1

Get the input number from the user.

2

Use the built-in function to calculate the square root of the number.

3

Display the result to the user.

Code

csharp

using System;
class Program {
    static void Main() {
        Console.Write("Enter a number: ");
        double number = Convert.ToDouble(Console.ReadLine());
        double squareRoot = Math.Sqrt(number);
        Console.WriteLine($"Square root of {number} is {squareRoot}");
    }
}

Output

Enter a number: 16
Square root of 16 is 4

Dry Run

Let's trace the input 16 through the code

1

Input number

User enters 16, so number = 16

2

Calculate square root

squareRoot = Math.Sqrt(16) which equals 4

3

Output result

Prints 'Square root of 16 is 4'

Step	Variable	Value
1	number	16
2	squareRoot	4
3	output	Square root of 16 is 4

Why This Works

Step 1: Reading input

We read the number from the user using Console.ReadLine() and convert it to a double for decimal support.

Step 2: Calculating square root

We use Math.Sqrt() which is a built-in C# method that returns the square root of the given number.

Step 3: Displaying result

We print the result using Console.WriteLine() with string interpolation to show the original number and its square root.

Alternative Approaches

Using exponentiation operator

csharp

using System;
class Program {
    static void Main() {
        Console.Write("Enter a number: ");
        double number = Convert.ToDouble(Console.ReadLine());
        double squareRoot = Math.Pow(number, 0.5);
        Console.WriteLine($"Square root of {number} is {squareRoot}");
    }
}

This uses <code>Math.Pow</code> with 0.5 as the exponent to find the square root, which is mathematically equivalent but slightly less direct than <code>Math.Sqrt</code>.

Manual approximation (Newton's method)

csharp

using System;
class Program {
    static double SqrtNewton(double n) {
        double x = n;
        double y = 1;
        double e = 0.00001; // precision
        while (x - y > e) {
            x = (x + y) / 2;
            y = n / x;
        }
        return x;
    }
    static void Main() {
        Console.Write("Enter a number: ");
        double number = Convert.ToDouble(Console.ReadLine());
        double squareRoot = SqrtNewton(number);
        Console.WriteLine($"Square root of {number} is {squareRoot}");
    }
}

This method approximates the square root using Newton's iterative method, useful for learning but less efficient than built-in functions.

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

Time Complexity

Using Math.Sqrt is a constant time operation because it uses optimized CPU instructions or library calls.

Space Complexity

The program uses a fixed amount of memory for variables, so space complexity is constant.

Which Approach is Fastest?

Math.Sqrt is fastest and most reliable; manual methods like Newton's are slower and mainly educational.

Approach	Time	Space	Best For
Math.Sqrt	O(1)	O(1)	Fast, simple, built-in
Math.Pow with 0.5	O(1)	O(1)	Alternative, less direct
Newton's method	O(k) where k is iterations	O(1)	Learning approximation, no built-in