Skill: Represent perfect squares

A perfect square is a whole number made by multiplying a whole number by itself:

$$n^2=n\times n$$

To represent a perfect square, you can show:

• equal rows and columns in an array,
• the area of a square, or
• exponential form.

Example: Represent $36$.

1. Find a whole number that multiplies by itself to make $36$:

$$6\times6=36$$

2. Write it in exponential form:

$$6^2=36$$

3. Show it as an array with $6$ rows and $6$ columns:

$$\begin{array}{cccccc} \square&\square&\square&\square&\square&\square\\ \square&\square&\square&\square&\square&\square\\ \square&\square&\square&\square&\square&\square\\ \square&\square&\square&\square&\square&\square\\ \square&\square&\square&\square&\square&\square\\ \square&\square&\square&\square&\square&\square \end{array}$$

4. Think of the array as a square with side length $6$. Its area is:

$$6\times6=36$$

Therefore, $36$ is a perfect square because it can be written as $6\times6$, or $6^2$.