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Square Numbers

Square Numbers

The term 'square number' may seem a little intimidating at first, but it is actually very simple!

What is a square number?

A square number is the product of a whole number which has been multiplied by itself.

For example, 16 and 25 are both square numbers because they are the result of multiplying 4 × 4 and 5 × 5, respectively.

Square Number Calculation
16 4 × 4
25 5 × 5

Why is it called a 'square number'?

These numbers are named square numbers because, in visual representations, all square numbers can form a square.

Square number Visual representation
4 2 x 2 grid visual representation to help with square number understanding
9 3 x 3 grid visual representation to help with square number understanding
16 4 x 4 grid visual representation to help with square number understanding
25 5 x 5 grid visual representation to help with square number understanding

How do I square a number?

When a number is 'squared' it is simply multiplied by itself.

In calculations, numbers to be squared are written using the squared symbol or squared notation, a small 2 placed next to the number to be squared.

The table below shows several examples:

Squared Notation Calculation Square Number
42 4 × 4 16
62 6 × 6 36
82 8 × 8 64
102 10 × 10 100

What are the first 12 square numbers?

Below is a square numbers list up to 144:

1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th
1 4 9 16 25 36 49 64 81 100 121 144

Children should know or be able to calculate, the first twelve square numbers using their times tables. Primary aged children are expected to know their times tables up to 12 × 12 by the end of Year 4.

All square numbers from 1 – 1000

There are 31 square numbers between 1 and 1000:

1 81 289 625
4 100 324 676
9 121 361 729
16 144 400 784
25 169 441 841
36 196 484 900
49 225 529 961
64 256 576

Why do children need to know about square numbers?

Firstly, because the national curriculum expects them to! KS2 SATs questions will often ask children to square numbers or "find the squares" within a list of numbers. An awareness of square numbers also helps children find the square root of a number.

Also, understanding square numbers is very useful in maths. Topics such as areas, volumes and lengths of sides in shapes often involve square numbers. Understanding square numbers also helps children tackle the KS3 topic cubed numbers!

When do children learn about square numbers?

Children begin learning about square numbers in Year 5. They then continue to build their understanding in Year 6, learning how and when to use them.

Key Points

  • Square numbers are the result of multiplying a whole number by itself.
  • The squared symbol is a small '2' e.g. 32, 42, 52, 62 etc
  • To 'square' a whole number simply multiply it by itself.
  • Square numbers form a square in visual representations.