# What Is a Square Number? (Mathematics Glossary)

# What Is a Square Number?

A square number is a number that results from a number being multiplied by itself.For example,

- 1 is a square number. It is 1 × 1.
- 4 is a square number. It is 2 × 2.
- 9 is a square number. It is 3 × 3.

**Note:**2 × 2 can be written 2

^{2}("2 squared"),

#### Dictionary Definition

The Oxford English Dictionary defines a square number as "the product of a number multiplied by itself."# The Square Numbers

The square numbers are:In a number square, the square numbers are shaded below:

These are just the square numbers up to 100. There are infinitely many square numbers, they go on forever.

# How to Find Square Numbers

Finding square numbers is easy. Just multiply a number by itself.The first 10 square numbers are found by multiplying 1 by itself, then 2 by itself, as shown below.

# Square Numbers in Algebra

In algebra, letters are used instead of numbers.Just as we can square a number...

2

...we can square a letter:^{2}= 2 × 2 = 4
x

^{2}= x × x**Note:**We would say x

^{2}as "x squared", just like we would say 2

^{2}as "2 squared".

Here are some examples of squared letters in algebra:

- Quadratic equations have an x
^{2}term:

- Pythagoras theorem relates the square of the lengths of the sides of a right triangle to each other.

The image below shows the formula for Pythagoras theorem and the lengths of the sides**a**,**b**and**c**of a right triangle:

- The area of a circle is related to the square of its radius.

The image below shows the formula for the area of a circle and the circle's radius,**r**

##### Interactive Test

**show**

Here's a second test on square numbers.

Here's a third test on square numbers.

Here's a dynamic test on square numbers.

##### Note

# Square Numbers Come From Integers

Square numbers are the result of integers (whole numbers, not fractions) being multiplied by themselves.A square number will always be an integer.

# Square Numbers Are Always Positive

A square number is always a positive number. They can never be a negative number.Negative numbers can be multiplied by themselves to give a positive square number:

-2 × -2 = (-2)

^{2}= 4# "Squaring" a Number

The verb which describes the operation of multiplying a number by itself (e.g. 6 × 6) is "to square".When we multiply a number be itself , we call this "squaring" a number.

6 × 6 = 6

^{2}(called "6 squared").

# Why "Square" Numbers?

A square number is a number times itself.
1

2

3

^{2}= 1 × 1 = 12

^{2}= 2 × 2 = 43

^{2}= 3 × 3 = 9*The squares go 1, 4, 9...*

A square with sides of length 1 has an area of 1.

A square with sides of length 2 has an area of 4.

A square with sides of length 3 has an area of 9.

*The areas go 1, 4, 9...*

The square of a number and the area of a square with side lengths of that number are the same.

# Square Roots

If 2² = 4, then 4 is the square of 2.The inverse of the square is the square root, denoted by the √ symbol.

2 is the square root of 4, or √4 = 2.