When a value is followed by the term "squared," it means that the value is being raised to the power of two. For example, two squared is written as follows:

In the above figure, "squared" refers to the exponent, 2.

Squaring a value (raising it to the power of 2) just means to multiply the number by itself: 22 = 2 × 2 = 4. One way to visualize this is to use a square. Think of numerals as squares with side lengths of 1 unit, so 2 × 2 forms a square where each side is made up of 2 squares with 1 unit side lengths:

In this manner, we can see that a square with side lengths of 2 is comprised of 4 squares. This is one way to view the concept of area, and is why many measurements of area are "square units," such as ft2, in2, m2, and more.

Perfect squares

A perfect square is the square of an integer. It can be helpful to memorize perfect squares, at least up to a certain number, because it can allow us to more easily perform a lot of basic arithmetic. Below is a table showing the perfect squares from 0-20.

Integer Squares
0 0
1 1
2 4
3 9
4 16
5 25
6 36
7 49
8 64
9 81
10 100
11 121
12 144
13 169
14 196
15 225
16 256
17 289
18 324
19 361
20 400

Squares of negative numbers

The square of a number is always positive regardless of whether the number being squared is negative or positive. This is because a negative number multiplied by a negative number is positive, and a square is a number multiplied by itself, so the square of a negative number will always be positive.

This is important when solving algebraic equations that involve square roots.


In this example, we know that x can be either -2 or 2, since the square of either is 4.