No doubt during your KS3 Maths lessons you've come across powers. You may even have done our quiz on the subject. Powers are the small numbers above and to the right of another number. Basically, they tell you to multiply that number by itself as many times as the power requires.

The power you will come across most often in algebra is the square. This is the most basic power and it means that you should multiply the number by itself just the once. So, if square numbers are the result of multiplying numbers by themselves, then you'll know quite a few already from your times tables. As an example 5^{2} means 5 x 5 which everyone knows is 25.

See how much you remember from your lessons by playing the following quiz on square numbers. Read each question carefully and take your time. And don't forget the helpful comments after each question. They can help to clarify anything you are unsure of,

1.

What is 0^{2}?

0

2

4

8

No matter how many times you multiply 0 x 0 it will still be 0!

2.

A patch of garden is 10 metres x 10 metres. What is its area expressed in square metres?

2^{10}

10^{2}

2 x 10

10 x 2

3.

What number is 3^{2}?

3

6

9

12

Multiply 3 by itself (3) and you get 9

4.

What is the missing square number in the sequence 1, 4, 9, 16, 25, 36, 49, ......., 81?

56

60

64

68

64 is 8 x 8; on one side it has 7 x 7 (49) and on the other side it has 9 x 9 (81)

5.

What is the next square number after 9?

12

14

16

18

3 x 3 is 9; 4 x 4 is 16

6.

What is 1^{2}?

0

1

2

3

1 x 1 = 1

7.

What is the square number that comes immediately before 36?

10

15

20

25

6 x 6 is 36; 5 x 5 is 25

8.

Is the number 13,692 a square number?

Yes

No

Only in algebra

Always, except in algebra

A square number (also called a perfect square) is a positive whole number that is formed by multiplying a whole number with itself. For example, 16 = 4 x 4; 1 = 1 x 1; 1,681 = 41 x 41, and so on

9.

How would you refer to 3^{2}?

Large 3, little 2

3, superscript 2

3 multiplied by 2

3 squared

You might say '3 to the power of 2' but it is more usual to say '3 squared'

10.

The roof of a rabbit hutch is completely tiled. There are 7 tiles across and 7 tiles down. How many tiles are there altogether?

14

28

42

49

Can you see why the number of tiles might be referred to as 7^{2}?