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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 is 1²?

1 x 1 = 1

2 .

Is the number 13,692 a square number?

Yes

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

3 .

What is 0²?

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

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 .

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

Can you see why the number of tiles might be referred to as 7²?

7 .

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

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)

8 .

What is the square number that comes immediately before 36?

6 x 6 is 36; 5 x 5 is 25

9 .

What number is 3²?

Multiply 3 by itself (3) and you get 9

10 .

What is the next square number after 9?

3 x 3 is 9; 4 x 4 is 16

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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