Square Root Simple Calculator

The square root of a number is a value that, when multiplied by itself, gives the original number. This calculator helps you find square roots quickly and accurately.

What is a square root?

The square root of a number x is written as √x. It's the non-negative number that, when multiplied by itself, equals x. For example, √9 = 3 because 3 × 3 = 9.

Square roots are fundamental in mathematics, engineering, and many scientific fields. They appear in calculations involving areas, distances, and more.

How to calculate square roots

There are several methods to find square roots:

Prime factorization: Break down the number into prime factors and pair them.
Long division method: A step-by-step algorithm for finding square roots.
Calculator method: Use a calculator for quick results.
Estimation: Use known squares to approximate the answer.

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

Square root formula

The square root of a number x can be represented by the formula:

√x = y
where y × y = x

For example, if x = 16, then y = 4 because 4 × 4 = 16.

Worked examples

Example 1: √25

Find the square root of 25.

√25 = 5
because 5 × 5 = 25

Example 2: √144

Find the square root of 144.

√144 = 12
because 12 × 12 = 144

Example 3: √2

Find the square root of 2.

√2 ≈ 1.41421356237
because 1.41421356237 × 1.41421356237 ≈ 2

Frequently asked questions

What is the square root of 0?

The square root of 0 is 0 because 0 × 0 = 0.

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, it's possible.

Is the square root of 1 equal to 1?

Yes, because 1 × 1 = 1.

What is the square root of a fraction?

The square root of a fraction a/b is √a/√b.