X Tables
Times Table Methods

Square numbers in the times tables

Spot 1, 4, 9, 16, 25 and other square products in the multiplication grid.

Quick answer

Square numbers in the times tables are the products you get when you multiply a number by itself. For example, 3 × 3 = 9, so 9 is a square number. You can spot them in the multiplication grid by looking for numbers that appear twice in the same row and column.

Learning outcome

By the end of this page, you will be able to identify square numbers in the times tables and understand how they are made by multiplying a number by itself. Success signs:
  • You can name the first 10 square numbers.
  • You can find square numbers in a multiplication grid.
  • You can explain how 4 × 4 = 16 using equal groups or an array.
  • You can spot square numbers in real-life situations.

Why this matters

Square numbers help you understand multiplication better and are useful in many real-life situations. You might use them when planning a garden, making a square puzzle, or counting how many tiles are needed for a square floor. They also help with more advanced maths like algebra and geometry. Knowing square numbers makes you better at solving puzzles and problems in games, sports, and everyday life.

How it works

Square numbers are made by multiplying a number by itself. For example:
  • 1 × 1 = 1
  • 2 × 2 = 4
  • 3 × 3 = 9
  • 4 × 4 = 16
  • 5 × 5 = 25
You can also think of square numbers as equal groups of the same size. For example, 4 × 4 means 4 groups of 4 items each. If you draw this, you get a square shape made of dots or blocks.

Examples you can see

Let's look at how to find square numbers in a multiplication grid. Example 1: The 3 times table
  • 3 × 1 = 3
  • 3 × 2 = 6
  • 3 × 3 = 9
  • 3 × 4 = 12
The square number here is 9, because 3 × 3 = 9. Example 2: Drawing arrays Imagine you have 4 rows of 4 stickers each. How many stickers do you have?
  • Row 1: 4 stickers
  • Row 2: 4 stickers
  • Row 3: 4 stickers
  • Row 4: 4 stickers
That’s 4 × 4 = 16 stickers. You can also draw a square with 4 rows and 4 columns to show this. Example 3: Real-world square numbers If you are making a square garden with 5 plants in each row and 5 plants in each column, how many plants do you need?
  • 5 × 5 = 25 plants
This is a square garden, and 25 is a square number.

Try it as a mini adventure

Adventure: The Square Garden Quest You are a gardener and you need to plant a square garden. You want it to be 3 plants wide and 3 plants tall. How many plants do you need?
  1. First, you count the rows: 3 rows
  2. Each row has 3 plants
  3. So you need 3 × 3 = 9 plants
Now, try to build your garden with 4 rows and 4 plants in each row.
  1. How many plants do you need now?
  2. Can you draw a square to show your garden?
Next, try 5 rows and 5 plants in each row.
  1. How many plants do you need?
  2. Can you write it as a multiplication sentence?

Common mistakes

  • Mistake: Thinking 2 × 2 = 4, but confusing it with 2 + 2 = 4.
    Why it happens: Children might mix up addition and multiplication.
    Fix: Remember that multiplication means groups of the same size. 2 × 2 means 2 groups of 2, not 2 plus 2.
  • Mistake: Forgetting that 1 × 1 = 1.
    Why it happens: It seems too simple to remember.
    Fix: Practice saying 1 × 1 = 1 a few times. It's the first square number!
  • Mistake: Not seeing that 6 × 6 = 36 is a square number.
    Why it happens: It's easy to forget that square numbers are products of the same number.
    Fix: Use arrays or draw a square to show 6 × 6 = 36.

Parent and carer guide

As a parent or carer, you can help your child by:
  • Playing a game where you ask them to find square numbers in a multiplication grid.
  • Using everyday examples like tiles on the floor or plants in a garden.
  • Practising by asking your child to count how many items are in a square array (like 5 rows of 5).
  • Reinforcing that 3 × 3 = 9 means 3 groups of 3, and drawing this to help them see the square shape.
  • Encouraging them to say the square numbers out loud: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.
Don't worry if they make a mistake. It's part of learning. Celebrate their effort and help them understand the correct way.

Practice questions

  1. What is 2 × 2?
  2. What is 5 × 5?
  3. Which of these is a square number: 10, 12, 16, 18?
  4. How many plants are needed for a 4 × 4 garden?
  5. What is 7 × 7?
Answers:
  1. 4
  2. 25
  3. 16
  4. 16
  5. 49

FAQ

What are square numbers?

Square numbers are the result of multiplying a number by itself. For example, 4 is a square number because 2 × 2 = 4.

Why are they called "square" numbers?

They are called square numbers because they can be arranged into a square shape, like 3 rows of 3 dots.

Are all square numbers even?

No, square numbers can be odd or even. For example, 3 × 3 = 9 (odd) and 4 × 4 = 16 (even).

How do I remember square numbers?

You can remember them by practicing the times tables and drawing arrays to see the square shape.

What is the biggest square number in the times tables?

The biggest square number in the 12 times table is 12 × 12 = 144.

Number Multiplication Square Number
0 0 × 0 0
1 1 × 1 1
2 2 × 2 4
3 3 × 3 9
4 4 × 4 16
5 5 × 5 25
6 6 × 6 36
7 7 × 7 49
8 8 × 8 64
9 9 × 9 81
10 10 × 10 100
11 11 × 11 121
12 12 × 12 144