Square and Cube Numbers | KS3 Maths

That small raised number tells you how many of the number to multiply together — and the names give the game away. $5^2$ is literally a 5 by 5 square of tiles, and $4^3$ is a 4 by 4 by 4 cube of blocks. Once you've seen the shapes, both the names and the answers make sense.

Why is it called "squared"?

Worked example

What is 5 squared?

$5$ squared means a square with 5 along each side. Build it and count the tiles: 5 rows of 5.

$5^2 \;=\; 5 \times 5 \;=\; 25$

That's where the name comes from — you are literally making a square. And the little $2$ is telling you how many fives to multiply, not something to multiply by. This one picture is what stops $5^2 = 10$ from ever happening again.

And "cubed"?

Worked example

What is 4 cubed?

Exactly the same idea, one dimension up: $4$ cubed means a cube with 4 along every edge.

One layer of that cube is $4 \times 4 = 16$ blocks. And there are 4 layers, so:

$4^3 \;=\; 4 \times 4 \times 4 \;=\; 64$

Squares and cubes: 1 to 10

These are worth knowing on sight — they turn up constantly, and knowing them forwards also gives you square and cube roots backwards.

Look at 64: it appears in both columns, as $8^2$ and as $4^3$. It's the one number in this range that is both a square and a cube.

Going further: which is bigger, 2⁵ or 5²?

Worked example

2 to the power 5, or 5 squared?

The rule generalises past squares and cubes — the small number always says how many to multiply:

$2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32 \qquad 5^2 = 5 \times 5 = 25$

Doubling up gives $2, 4, 8, 16, 32$. So $2^5 > 5^2$ — 32 beats 25, even though $5$ is the bigger number to start with. More twos beats a bigger number, which is worth remembering when you meet indices properly.

Where you'll use this next

• Square and cube roots run this backwards: given the answer, find the number you squared.
• Area and volume are squares and cubes with units — a square 5 cm on each side has area $5^2 = 25$ cm².
• Index laws and standard form build directly on what that small raised number means.

Practice questions

Try these yourself, then click to check each answer. Ask "how many of them am I multiplying?" every time.