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Level 3-4 Algebra - Square Numbers
The square number immediately after 16 is 25.

Level 3-4 Algebra - Square Numbers

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 .
What number is 32?
3
6
9
12
Multiply 3 by itself (3) and you get 9
2 .
What is the square number that comes immediately before 36?
10
15
20
25
6 x 6 is 36; 5 x 5 is 25
3 .
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
4 .
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
5 .
How would you refer to 32?
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'
6 .
What is 12?
0
1
2
3
1 x 1 = 1
7 .
What is the next square number after 9?
12
14
16
18
3 x 3 is 9; 4 x 4 is 16
8 .
What is 02?
0
2
4
8
No matter how many times you multiply 0 x 0 it will still be 0!
9 .
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)
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 72?
You can find more about this topic by visiting BBC Bitesize - What are square and cube numbers

Author:  Frank Evans (Specialist 11 Plus Teacher and Tutor)
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