# Square Numbers

## What Is a Square Number?

A square number is a number that results from a number being multiplied by itself.

For example,

• 1 is a square number. It is 1 × 1.

• 4 is a square number. It is 2 × 2.

• 9 is a square number. It is 3 × 3.

Note: 2 × 2 can be written 22 ("2 squared").

### Dictionary Definition

The Oxford English Dictionary defines a square number as "the product of a number multiplied by itself."

## The Square Numbers

The square numbers are: In a number square, the square numbers are shaded below: These are just the square numbers up to 100. There are infinitely many square numbers, they go on forever.

## How to Find Square Numbers

Finding square numbers is easy. Just multiply a number by itself.

The first 10 square numbers are found by multiplying 1 by itself, then 2 by itself, as shown below. ## Square Numbers in Algebra

In algebra, letters are used instead of numbers.

Just as we can square a number...

22 = 2 × 2 = 4

...we can square a letter:

x2 = x × x

Note: We would say x2 as "x squared", just like we would say 22 as "2 squared".

Here are some examples of squared letters in algebra:

• Quadratic equations have an x2 term: • Pythagoras theorem relates the square of the lengths of the sides of a right triangle to each other.

The image below shows the formula for Pythagoras theorem and the lengths of the sides a, b and c of a right triangle: • The area of a circle is related to the square of its radius.

The image below shows the formula for the area of a circle and the circle's radius, r: 