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