# SAT / ACT Prep Online Guides and Tips What is a perfect square? How do you know if a number is a perfect square?

In this article, we’ll define perfect squares, provide a list of the first 25 perfect squares (and the integers that make them up), and teach you how to tell if a number is a perfect square.

## What Is a Perfect Square?

A perfect square is a number that can be expressed as the product of two equal integers.

What does that mean?

Basically, a perfect square is what you get when you multiply two equal integers by each other.

For instance:

\$\$5 * 5 = 25\$\$

25 is a perfect square because you’re multiplying two equal integers (5 and 5) by each other.

You can also express \$5 * 5\$ as \$5^2\$. That’s where you get the term “perfect square”

## List of Perfect Squares

Here’s a list of the first 25 perfect squares. A hint: if you want to create a perfect square, simply square an integer!

 Square Integers 1 \$1 * 1\$ 4 \$2 * 2\$ 9 \$3 * 3\$ 16 \$4 * 4\$ 25 \$5 * 5\$ 36 \$6 * 6\$ 49 \$7 * 7\$ 64 \$8 * 8\$ 81 \$9 * 9\$ 100 \$10 * 10\$ 121 \$11 * 11\$ 144 \$12 * 12\$ 169 \$13 * 13\$ 196 \$14 * 14\$ 225 \$15 * 15\$ 256 \$16 * 16\$ 289 \$17 * 17\$ 324 \$18 * 18\$ 361 \$19 * 19\$ 400 \$20 * 20\$ 441 \$21 * 21\$ 484 \$22 * 22\$ 529 \$23 * 23\$ 576 \$24 * 24\$ 625 \$25 * 25\$

## How to Tell If a Number Is a Perfect Square

You can tell if a number is a perfect square in a couple of different ways.

First of all, if you create a square by multiplying two equal integers by each other, then the product is a perfect square.

So, \$1 * 1\$ is a perfect square. So is \$10 * 10\$ and \$1,000 * 1,000\$.

You can also tell if a number is a perfect square by finding its square roots. Finding the square root is the inverse (opposite) of squaring a number.

If you find the square root of a number and it’s a whole integer, that tells you that the number is a perfect square.

For instance, the square root of 25 is 5. The square root of 26 is not a whole integer. So, 26 is not a perfect square. ## Key Takeaways: Understanding Perfect Squares

A perfect square is a number that can be expressed as the product of two equal integers.

You can tell if a number by finding its square root and seeing if that square root is a whole integer.

## What's Next?

Getting ready to take the ACT? We have a list of 31 formulas you must know to conquer the ACT.

Taking the SAT instead? Here’s a list of our favorite SAT Math prep books that will help set you on the path to success.

Looking to brush up on your fundamental algebra skills? A good place to start is mastering systems of equations. 