What Is a Square Number?
A square number is a number that results from a number being multiplied by itself.
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").
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:
The image below shows the formula for Pythagoras theorem and the lengths of the sides a, b and c of a right triangle:
The image below shows the formula for the area of a circle and the circle's radius, r: