Perfect Squares and Square Roots

Contributor: Briana Pincherri. Lesson ID: 11509

You wouldn't want to be called a perfect square, but you do need to understand what a perfect square and square root are in math! Easy-to-understand videos and online practice round out your learning!


Expressions and Equations, Pre-Algebra

learning style
personality style
Lion, Otter
Grade Level
Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!

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Don't roots only grow in the ground? No way! They come up in math topics, too!

Before you jump into square roots, let's make sure you understand what a perfect "square" number is.

A perfect square is a number that is the product of two equal integers — or, in other words, it is the ANSWER when the same integer is multiplied times itself.

For example: 4 x 4 = 16. The 16 is a perfect square.

  • Can you name three more perfect square numbers?

(If you are stumped, just pick any integer and multiply it times itself. The ANSWER is a perfect square.)

A number is ONLY a perfect square if the square root of it is an integer (no decimals). But, what are square roots? Watch this Math Antics – Exponents & Square Roots video to review exponents, find out what a square root is, and to understand how they connect:

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  • What are two things you learned from the video?
  • How do exponents and squares relate?

Now, grab your math notebook and get ready to take a few notes and try some problems.

  • So, what is a square root?

Square root A number that produces a specific quantity when multiplied by itself.

The symbol to take the square root looks like this √ and is called a radical.

To find the square root:

  • Ask yourself, "What number times itself equals the number given?"
  • Punch the number in a calculator and hit the square root button.


Some work out very "neatly," while others have a long decimal answer.

  √16 = 4 4 x 4 = 16
  √144 = 12 12 x 12 = 144
  √28 = 5.29....  
  √212 = 14.56....  


As noted in the video, it is also possible to take the 3rd root of a number 3√, 4th root of a number 4√, the 5th root of a number 5√, and so on. You use the radical symbol with a number just above it.

It means, "What number can you take times itself that many times (the number above the radical sign) to get the given number?"


  • Think: What number times itself 3 times is 125?
  5 x 5 x 5 = 125


Now that you have had a chance to learn about perfect square numbers and square roots, it is time for a little practice. Let's see just how well you have "Got It?" in the next section!

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