Simplifying Square Roots
 GOAL: I can simplify perfect square roots without using a calculator

 Learning Standards  Common Core Standard: 7.EE.1


RED BOOK Reference:

Pages: 103 ─ 107

 Practice on page 107,
#20-27 all.
BLACK BOOK Reference:
Pages: 16 ─ 20

Practice on page 20,
#9-18 all.

 Practices (with answers)  
  Simplifying Square Roots (ver. 1)

  Simplifying Square Roots (ver. 2)

Simplifying Square Roots  (ver. 3)

 Lesson Vocabulary  
 Square Root The square root of a number is a value that, when multiplied by itself, gives the number.
 Perfect Squares Numbers whose square roots are integers (no decimals).

 Video Tutorials    
Topic Description  Time (min: sec)
Understanding Square Roots  Khan Academy 1:21
 (interactive practice)
Square Roots
 Khan Academy 

Strategies and Content Practice 
 What do you recall about squaring a numbers?
 How do you suppose squaring a number is related to the square root of a number?
Engage The square roots that most people are familiar with are the ones that come from memorizing the times tables.  These square root values produce integer square roots.  Keep in mind though that there are an infinite number of square root answers and nearly all of them are NOT integers, in other words, they are decimals.

The square root is defined as "
a value that, when multiplied by itself, gives the number".
For example, 6 • 6 = 36.
So we would say, "The square root of 36 is 6."

Another example, 8 • 8 = 64.
So we would say, "The square root of 64 is 8."

The numbers 36 and 64 are sometimes called perfect squares because their square roots
(6 and 8) are integer numbers (no decimals).

As a comparison, let's take the square root of a non-perfect square number like 20.
The square root of 20, √20 = 4.472135955..........

So you can see that most of the numbers we can take the square root of will have decimal answers.

After example problems and videos, try to solve the Practice Worksheets above.  The answers to the practices are on the last page so you can check how well you are doing.

Please see me for more help if you are having difficulty with the practices.