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Square and cube numbers

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Explainer Video

Tutor: Labib

Summary

Square and cube numbers

In a nutshell

Square and cube numbers are given the name square and cube because the area of a square is a number multiplied by itself once whilst the volume of a cube is a number multiplied by itself twice. There are $10$ square numbers and $4$ cube numbers between $1$ and $100$ .

Square numbers

Square numbers are made when a number is multiplied by itself once. The symbol to show a square number is $^2$ so, $3^2$ means $3$ squared or $3\times3$ .

Example 1

What are the first $5$ square numbers?

$\begin{aligned}1^2 &= 1 \times 1 = 1 \\ 2^2 &= 2 \times 2 = 4 \\ 3^2 &= 3 \times 3 = 9 \\ 4^2 &= 4 \times 4 = 16 \\ 5^2 &= 5 \times 5 = 25 \end{aligned}$

The first five square numbers are $\underline{1,4,9,16,25}$ .

Cube numbers

Cube numbers are made when a number is multiplied by itself twice . The symbol to show a cube number is $^3$ so, $3^3$ means $3$ cubed or $3\times3 \times 3$ .

Example 2

What are the first $3$ cube numbers?

$\begin{aligned}1^3 &= 1 \times 1 \times 1 = 1 \\ 2^3 &= 2 \times 2 \times 2= 8 \\ 3^3 &= 3 \times 3 \times 3 = 27 \end{aligned}$ 

The first three cube numbers are $\underline{1,8,27}$ .

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Unit 1