A square root of a number is a value that, when multiplied by itself, gives the original number.

In simple terms:
👉 A square root “undoes” squaring a number.

Basic Definition

The square root of a number $n$ is written as:

sqrt{n}​

It means:

a number × the same number = n

Examples

• $3$ because 3×3=9

• sqrt{16} = 4 because $16$

• sqrt{25} = 5​ because 5×5=25

Perfect Squares

A perfect square is a number that is the square of a whole number.

Examples:

• 1 = 1^2

• 4 = 2^2

• 9 = 3^2

• 16 =  4^2

• 25 = 5^2

Perfect squares have whole-number square roots.

Square Roots That Are Not Whole Numbers

Not all numbers have whole-number square roots.

Example:

sqrt{2} ​≈ 1.41

This is an irrational number, meaning it does not end or repeat.

Positive and Negative Square Roots

• Every positive number has two square roots: one positive and one negative.

• Example:

sqrt{9} ​=±3

But when we write sqrt{9}​, we usually mean the principal (positive) square root, which is 3.

Square Roots and Exponents

Square roots are related to exponents:

sqrt(n) = n^(1/2)​

Example:

$$4$$

Why Are Square Roots Important?

• Used in geometry (finding side lengths)

• Used in science and engineering

• Help solve equations

• Appear in real-life measurements