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!

categories

Middle School

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

Lesson Plan - Get It!

Audio:

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:

 

Find a parent or teacher and tell them two things you learned from the video. Try to explain how exponents and squares relate. Once you are done discussing, 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.

Examples

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?"

Example

  3√125
 
  • 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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