Mathisfun Square Root Calculator

The Mathisfun Square Root Calculator helps you find the square root of any positive number. Whether you're solving math problems, checking your work, or just curious about square roots, this tool provides quick and accurate results.

What is a Square Root?

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4 × 4 = 16. Square roots are represented by the radical symbol √.

For a number x, the square root is written as √x.

Square roots can be positive or negative, but the principal (or positive) square root is typically used in most calculations. For example, √9 = 3, not -3.

How to Calculate Square Roots

There are several methods to calculate square roots:

Prime Factorization: Break down the number into its prime factors and pair them.
Long Division Method: A step-by-step process similar to long division.
Using a Calculator: The quickest method for most people.

Our calculator uses the most efficient method available in JavaScript to provide accurate results instantly.

Note: The calculator only accepts positive numbers. Attempting to calculate the square root of a negative number will result in an error.

Examples

Let's look at a few examples to understand how square roots work:

√16 = 4 (since 4 × 4 = 16)
√25 = 5 (since 5 × 5 = 25)
√9 = 3 (since 3 × 3 = 9)

For non-perfect squares like √2, the result is an irrational number approximately equal to 1.41421356237.

FAQ

What is the difference between a square root and a square?

A square is a number multiplied by itself (e.g., 5 squared is 25). A square root is a number that, when multiplied by itself, gives the original number (e.g., the square root of 25 is 5).

Can I find the square root of a negative number?

In real numbers, no. The square root of a negative number is not defined. However, in complex numbers, negative square roots exist.

Is the square root of a number always an integer?

No, only perfect squares (like 16, 25, 36) have integer square roots. Most numbers have irrational square roots.