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Chapter overview

Maths

Number and place value

Addition and subtraction

Multiplication and division

Fractions

Measurement

Geometry - properties of shapes

Geometry - position and direction

Statistics

Maths

Square and cube numbers

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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 1010​ square numbers and 44 ​ cube numbers between 11  and 100100.​



Square numbers

Square numbers are made when a number is multiplied by itself once. The symbol to show a square number is 2^2 so, 323^2  means 33 squared or 3×33\times3.​


Example 1

What are the first 55 square numbers?


​12=1×1=122=2×2=432=3×3=942=4×4=1652=5×5=25\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 1,4,9,16,25‾\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 3^3​ so, 333^3​ means 33​ cubed or 3×3×33\times3 \times 3​.


Example 2

What are the first 33 cube numbers?


13=1×1×1=123=2×2×2=833=3×3×3=27\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 1,8,27‾\underline{1,8,27}.


Frequently Asked Questions (FAQ)

FAQs

  • Question: What is a cube number?

    Answer: Cube numbers are made when a number is multiplied by itself twice .

  • Question: What is a square number?

    Answer: Square numbers are made when a number is multiplied by itself once.

Theory

Exercises

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