# What Is a Square Number?

A square number is a number multiplied by itself.

For example, 9 is a square number. It is 3 times itself:
it is 3 × 3, which may be written as 32 (pronounced as "3 squared").

The square numbers are:

# How to Find Square Numbers

Question: What is the square of a number, n?

Step 1
Multiply the number n by itself.
n × n = n2.

This is the square of the number, n.

# A Real Example of How to Find Square Numbers

Question: What is the square of 6?

Step 1
Multiply 6 by itself.
6 × 6 = 36.

36 is the square of 6.

# Real Examples of Square Numbers

The first 10 square numbers are:

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

show

##### Note
WHY "SQUARE" NUMBERS?

A square number is a number times itself.

12 = 1 × 1 = 1
22 = 2 × 2 = 4
32 = 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.

# PROPERTIES OF SQUARE NUMBERS

A square number is an integer that is a square of integer. An integer is a whole number.

A square number cannot 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