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What Is A Square Number? Explained For Teachers, Parents And Kids

In this post we will be explaining what square numbers are, why they are called square numbers and providing all the information you’ll need to help your child get to grips with this area of math. We’ve also included some square number based questions for your child to tackle, so take a look!

What is a square number?

A square number is the result when a number has been multiplied by itself. For example, 25 is a square number because it is 5 groups of 5, or 5 x 5. This is also written as 52 (“five squared”). 100 is also a square number because it’s 102 (10 x 10, or “ten squared”).

Square number examples

Square number examples

5 examples of square numbers are 625 (25 x 25, 252), 90,000 (300 x 300,3002), 289 (17 x 17, 172), 1 (1 x 1, 12) and 2304 (48 x 48,  482)

Square numbers up to 12 x 12

The first 12 square numbers (and the ones children are most likely to know due to learning their times tables) are:

1 x 1 or 12= 1

2 x 2 or 22 = 4

3 x 3 or 32= 9

4 x 4 or 42= 16

5 x 5 or 52= 25

6 x 6 or 62= 36

7 x 7 or 72= 49

8 x 8 or 82= 64

9 x 9 or 92= 81

10 x 10 or 102= 100

11 x 11 or 112= 121

12 x 12 or 122= 144

The square numbers from 1 to 100 are: 1, 4, 9, 25, 36, 49, 64, 81, 100

Here’s a handy image you can save with the above information on:

square numbers up to 144

How do you square a number?

This is very simple. All you have to do is take the number, and multiply it by itself!

Why are they called ‘square’ numbers?

What are ‘square’ numbers? Why are they not called (insert shape here) numbers?

These are questions that many grade schoolers ask, but fortunately the answer is simple. This particular collection of numbers are called square numbers (or squared numbers) for the simple reason that they form the area of a square. As squares have equal sides, finding the area is simple – just “square” (multiply by itself) one of its sides!

For example, a square with side length 2cm would have an area of 4cm2 (as 22 = 4). In reverse, if we knew a square had an area of 9cm2, we’d know that each side would measure 3cm (as 32 = 9).

See the diagrams below to demonstrate these examples.

visual example of square numbers

Square numbers for kids: What will my child learn about square numbers in school?

One of the first places students will see square and cube numbers is when they learn about the order of operations (PEMDAS) and therefore learn the term ‘exponent’ (the term for the small numbers used for squared  (x2) and cubed (x3) numbers).

Students will look more closely at the concept of square and cube numbers when they start to connect their understanding of operations to geometry and measurement as they work with area, and eventually volume. They will also use their understanding of the properties of these shapes to complete problems using multiplication and division.

They may also be expected to construct equivalence statements (for example, 4 x 35 = 2 x 2 x 35; 3 x 270 = 3 x 3 x 9 x 10 = 92 x 10). This understanding fits with Standard of Mathematical Practice #7: Look for and make use of structure, as students recognize the structure of square numbers and the different ways they can be constructed and deconstructed. All of this work prepares them for algebra that they will explore throughout middle school and high school.

How do square numbers relate to other areas of math?

Square numbers are particularly useful when finding the area of squares. As children are first introduced to this concept, they may count squares to find the area. As their mathematical knowledge expands, students will be taught to solve and compare the area of rectangles (including squares).

Learning square numbers also gives children a firm foundation from which they can learn about cube or cubed numbers as they build on their knowledge.

Wondering about how to explain other key math vocabulary to your children? Check out our Elementary Math Dictionary for Kids, or try these math terms:

Square number practice questions

1) 72 =

2) 36 and 64 are both square numbers. They have a sum of 100. Find two square numbers that have a sum of 130.

3) Here is a sorting diagram for numbers. Write a number less than 100 in each space.

Sorting diagram for square numbers

4) Explain why 16 is a square number.

5) Answer this math problem that tests student’s application of their knowledge of square numbers:

Square numbers SATs question for upper elementary

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The content in this article was originally written by primary school teacher Sophie Bartlett and has since been revised and adapted for US schools by elementary math teacher Jaclyn Wassell.

Sophie Bartlett
Sophie Bartlett
Year 6 Teacher
Sophie teaches mixed age classes at a small school in central England. She is a self confessed grammar pedant and number nerd so we've welcomed her as a regular author and editor for Third Space Learning.

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