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What Is the List of Perfect Squares, and Why Do I Need It?

list of perfect squares: Boy writing a mathematical equation on the blackboard

Students at all levels of math need a list of perfect squares. Knowing the most common perfect squares makes it much easier to solve square roots, which show up in all kinds of math problems. But before we go into perfect squares, let's review the definition of square roots.

What Are Square Roots?

We start learning about square roots in pre-algebra. To find the square root of a number, for example, 225, you simply determine what number multiplied by itself equals 225:

list of perfect squares: Square root of 225

A few notes to remember about squared numbers and square roots:

First, to show a number is squared (multiplied by itself), you must include an exponent of 2. For example, you could write 225 as 15 ².

Second, the result of a squared number is always a positive integer. For example, squaring -4 results in 16. That’s because multiplying two negative numbers or variables together always results in a positive number or variable.

What Makes a Perfect Square?

Perfect squares are important because they’re an example of how to take the square root of a perfectly precise natural number. The square root of a perfect square must also be a natural number, meaning that it’s a non-decimal, non-fractional integer. Let's review examples of which numbers qualify as natural numbers and integers:

Natural numbers: 1, 2, 3, 4, 5, 6 …

List of Perfect Squares

Here is a list of perfect square numbers:

list of perfect squares: Perfect square of 1

list of perfect squares:: Perfect square of 2

list of perfect squares:: Perfect square of 3

list of perfect squares: Perfect square of 4

Perfect square of 5

Perfect square of 6

Perfect square of 7

Perfect square of 8

Perfect square of 9

Why a List of Perfect Squares Is Important

Having a list of perfect squares will be your saving grace through all levels of math. When you don't have a calculator at hand, you must rely on your knowledge of the most common square roots to get you through challenging equations and word problems. Understanding square roots and having the above list of perfect squares can help set you up for success.

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