What Are Square Numbers?

When you multiply a whole number by itself, you get a square number (also called a perfect square).

Square Number

The product of a whole number multiplied by itself. For example, $4 \times 4 = 16$ , so 16 is a square number. We write this as $4^{2} = 16$ , read as "four squared".

We call them square numbers because they can be arranged into a perfect square pattern of dots.

Here are the first several perfect squares:

$n$	$n^{2}$
1	1
2	4
3	9
4	16
5	25
6	36
7	49
8	64
9	81
10	100

Analogy

Imagine you're tiling a floor with square tiles. If you arrange tiles into a 5-by-5 grid, you need exactly 25 tiles — that's why 25 is called a "square" number. You can always form a perfect square shape!

Square Roots

The square root is the reverse operation of squaring. If $3^{2} = 9$ , then the square root of 9 is 3.

Square Root

The square root of a number $n$ is the value that, when multiplied by itself, gives $n$ . We write it using the symbol . For example, $9 = 3$ because $3 \times 3 = 9$ .

A key property of square roots is:
$n \times n = n$

For example: $36 \times 36 = 36$

Example

Find $169$ .

We need a number that multiplies by itself to give 169.

Try $13$ : $13 \times 13 = 169$ ✓

So $169 = 13$

Check: $169 \times 169 = 13 \times 13 = 169$ ✓

Exam Tip

To find a square root without a calculator, think: "What number times itself gives this answer?" You can use trial and improvement, starting with numbers you know. For larger numbers, your calculator has a button.

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