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Maths Quiz - Level 3-4 Algebra - Square Numbers (Questions)

Square numbers are results of multiplying a number by itself. Learn to recognise squares, use area models, and apply the difference of two squares in KS3 algebra.

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Fascinating Fact:

The difference between two square numbers, such as 25 − 9, can often be factorised, like (5 + 3)(5 − 3) = 8 × 2 = 16.

In KS3 Maths, square numbers link arithmetic and algebra. You’ll spot perfect squares, use area models to visualise n × n, and apply the identity a2 − b2 = (a + b)(a − b) to simplify or factorise expressions.

Key Terms

  • Square number: A number made by multiplying an integer by itself, e.g. 1, 4, 9, 16.
  • Perfect square: An integer that is a square number, like 36 = 62.
  • Difference of two squares: An expression of the form a2 − b2 which factorises to (a + b)(a − b).

Frequently Asked Questions (Click to see answers)

What is a square number in KS3 maths?

A square number is the result of an integer multiplied by itself. Examples are 12 = 1, 22 = 4, 32 = 9, 102 = 100.

How do you square a negative number correctly?

Use brackets and square the whole number: (−4)2 = (−4) × (−4) = 16. Without brackets, −42 means −(42) = −16.

What is the difference of two squares formula?

The identity is a2 − b2 = (a + b)(a − b). For example, 25 − 9 = 52 − 32 = (5 + 3)(5 − 3) = 8 × 2 = 16.

Try These Related Quizzes

1. How would you refer to 32?
[ ] Large 3, little 2
[ ] 3, superscript 2
[ ] 3 multiplied by 2
[ ] 3 squared
2. What number is 32?
[ ] 3
[ ] 6
[ ] 9
[ ] 12
3. What is 12?
[ ] 0
[ ] 1
[ ] 2
[ ] 3
4. What is 02?
[ ] 0
[ ] 2
[ ] 4
[ ] 8
5. 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
6. A patch of garden is 10 metres x 10 metres. What is its area expressed in square metres?
[ ] 210
[ ] 102
[ ] 2 x 10
[ ] 10 x 2
7. What is the next square number after 9?
[ ] 12
[ ] 14
[ ] 16
[ ] 18
8. What is the square number that comes immediately before 36?
[ ] 10
[ ] 15
[ ] 20
[ ] 25
9. Is the number 13,692 a square number?
[ ] Yes
[ ] No
[ ] Only in algebra
[ ] Always, except in algebra
10. What is the missing square number in the sequence 1, 4, 9, 16, 25, 36, 49, ......., 81?
[ ] 56
[ ] 60
[ ] 64
[ ] 68

You can find more about this topic by visiting BBC Bitesize - What are square and cube numbers

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Maths Quiz - Level 3-4 Algebra - Square Numbers (Answers)
1. How would you refer to 32?
[ ] Large 3, little 2
[ ] 3, superscript 2
[ ] 3 multiplied by 2
[x] 3 squared
You might say '3 to the power of 2' but it is more usual to say '3 squared'
2. What number is 32?
[ ] 3
[ ] 6
[x] 9
[ ] 12
Multiply 3 by itself (3) and you get 9
3. What is 12?
[ ] 0
[x] 1
[ ] 2
[ ] 3
1 x 1 = 1
4. What is 02?
[x] 0
[ ] 2
[ ] 4
[ ] 8
No matter how many times you multiply 0 x 0 it will still be 0!
5. 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
[x] 49
Can you see why the number of tiles might be referred to as 72?
6. A patch of garden is 10 metres x 10 metres. What is its area expressed in square metres?
[ ] 210
[x] 102
[ ] 2 x 10
[ ] 10 x 2
7. What is the next square number after 9?
[ ] 12
[ ] 14
[x] 16
[ ] 18
3 x 3 is 9; 4 x 4 is 16
8. What is the square number that comes immediately before 36?
[ ] 10
[ ] 15
[ ] 20
[x] 25
6 x 6 is 36; 5 x 5 is 25
9. Is the number 13,692 a square number?
[ ] Yes
[x] 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
10. What is the missing square number in the sequence 1, 4, 9, 16, 25, 36, 49, ......., 81?
[ ] 56
[ ] 60
[x] 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)
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