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 $$\underline{1,8,27}$$.