What is a Square Number?

When you multiply a whole number by itself, the result is called a square number (also known as a perfect square).

Square Number

A square number (or perfect square) is the product of a whole number multiplied by itself. For example, $4 \times 4 = 16$ , so 16 is a square number.

We use a special notation for this: the small raised 2 is called an exponent or power, and it tells us to multiply the number by itself.

$3^{2} = 3 \times 3 = 9$

We read $3^{2}$ as "three squared" or "the square of three".

Analogy

The name "square number" comes from geometry. If you arrange dots into a grid (array), square numbers always form a perfect square shape — the same number of rows and columns. A $3 \times 3$ grid has 9 dots in a perfect square arrangement!

The First Square Numbers

Here are the first ten square numbers. It's very useful to memorise these!

Number ( $n$ )	Squared ( $n^{2}$ )	Result
1	$1^{2} = 1 \times 1$	1
2	$2^{2} = 2 \times 2$	4
3	$3^{2} = 3 \times 3$	9
4	$4^{2} = 4 \times 4$	16
5	$5^{2} = 5 \times 5$	25
6	$6^{2} = 6 \times 6$	36
7	$7^{2} = 7 \times 7$	49
8	$8^{2} = 8 \times 8$	64
9	$9^{2} = 9 \times 9$	81
10	$1 0^{2} = 10 \times 10$	100

Exam Tip

Notice a pattern: the differences between consecutive square numbers are 3, 5, 7, 9, 11, ... (all odd numbers). This can help you check your work or extend the list quickly!

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