- 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.## Interactive Game on Square Numbers

Here is an interactive game to help you learn about square numbers.- You are the fish.
- Pop the bubbles with square numbers to collect red hearts. You need five to win.
- If a bubble with a square number reaches the top, you will lose a red heart.
- Avoid the bubbles with non-square numbers. If you pop one, you will lose one of your three lives.
- Good luck!
- The fish moves towards your clicks. (Hint: The farther the distance, the faster it moves.)

## 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**:

## 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

A square with sides of length 1 has an area of 1.^{2}= 1 × 1 = 1 2^{2}= 2 × 2 = 4 3^{2}= 3 × 3 = 9*The squares go 1, 4, 9...*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.## You might also like...

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