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 2^{2} ("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...
2^{2} = 2 × 2 = 4
...we can square a letter:
x^{2} = x × x
Note: We would say x^{2} as "x squared", just like we would say 2^{2} as "2 squared".
Here are some examples of squared letters in algebra:

Quadratic equations have an x^{2} 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: