# What are square numbers?

## What are square numbers?

**multiply a number by itself**, the result is a

**square number**:

**1 x 1 = 1 7 x 7 = 49**

2 x 2 = 4 8 x 8 = 64

3 x 3 = 9 9 x 9 = 81

4 x 4 = 16 10 x 10 = 100

5 x 5 = 25 11 x 11 = 121

6 x 6 = 36 12 x 12 = 144

2 x 2 = 4 8 x 8 = 64

3 x 3 = 9 9 x 9 = 81

4 x 4 = 16 10 x 10 = 100

5 x 5 = 25 11 x 11 = 121

6 x 6 = 36 12 x 12 = 144

and so on.

To write the mathematical formula for square numbers we add a small 2 next to and above the number, for example: 3

^{2}.

## Square numbers in Key Stage 2

**Children in Years 5 and 6 are expected to know all the above square numbers, plus the corresponding squares of multiples of 10 (20 x 20 = 400, 30 x 30 = 900, 40 x 40 = 1600, etc.).**

Knowledge of square numbers can help children when it comes to working out the area of a square. For example: they may be shown a square (not drawn to scale) and told the area of the square is 81cm². If they are asked to work out the length of each side, their knowledge of square numbers will mean they will know instantly that each side of the square is 9cm.

**puzzles and investigations involving square numbers**. Here are some examples:

*Karen has these number cards:*

*If she puts all the cards in a hat and picks one out at random, what is the probability she will pick a square number?*

Answer: since there are 3 square numbers: 49, 100 and 16, the probability she will pick a square number is 3/8.

Answer: since there are 3 square numbers: 49, 100 and 16, the probability she will pick a square number is 3/8.

*Two square numbers are added together to make another square number. What are they?*

One possible answer is 16 + 9 which equals 25.

One possible answer is 16 + 9 which equals 25.

## More like this

### JOIN OVER 250,000 PARENTS and get FREE worksheets, activities & offers from TheSchoolRun.com

### Password Requirements

- Password must contain at least one uppercase character.
- Password must contain at least 10 alphanumeric (letter or number) characters.
- Password must contain at least one lowercase character.
- Password must contain at least one digit.

### How to use TheSchoolRun

### Testimonials

'Thank you for providing a much-needed service for parents and one which really represented good value for money. I particularly loved your handwriting sections and the ‘Learning Journey’ links that you have created. There are not many services I would pay to subscribe to, and even less I would recommend, but yours is one which I did!'

*- Nicola, Aberdeenshire*

'I’m not on social media but just wanted to reach out and say I have been recommending you to everyone I know, with kids of course!

Your site has been fantastic. It’s not only teaching my little one things, it’s showing me how things should’ve been done when I was younger. I do wish you were around then, as your content is fantastic and my little boy looks forward to your daily worksheets. Learning definitely made fun.

People are so quick to moan these days, so I wanted to send an email to sing my praises. You’ve helped me become more organised with the schedule of things, but without the pressure I was putting myself under before. We have fun and learn.'

*- Katie, Sevenoaks*

'I'm finding your site an absolutely fantastic resource alongside the stuff being sent from my son's school. We love being able to keep track of his progress on his Learning Journey checklist!'

*- Claire, Kent*

'Thank you so very much for all the help your site is giving myself to aid my daughter's education at home. Truly, it makes her day enjoyable, structured and continuous.'

*- Julie, Northamptonshire*