Reducing Square Roots of non-Perfect Squares

Reducing Square Roots of non-Perfect Squares

Without a Calculator

What is a Perfect Square?

An Integer with an exact square root

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, ...

Multiple Select

Select all of the Perfect Squares from the choices below (check the square roots!)

• 38

• 48

• 144

• 256

Multiple Choice

Is 289 a Perfect Square? (check the square root!)

• Yes

• No

• I have no idea

Reducing non-Perfect Square Roots

This is simply a matter of factoring!

Steps for Reducing a Square Root

• Find the largest Square root that divides the number evenly

• Break the root into two seperate roots )one with a square root and one without)

• Reduce the Perfect Square Root

Multiple Choice

Which of the following is the correct Factor Pair to fully reduce

 $\sqrt{24}$  ?

• 2 x 12

• 3 x 8

• 4 x 6

Multiple Choice

Which Correctly shows

 $\sqrt{24}$  broken into two radical expressions?

•  $\sqrt{2}\sqrt{12}$  

•  $\sqrt{3}\sqrt{8}$  

•  $\sqrt{1}\sqrt{24}$  

•  $\sqrt{4}\sqrt{6}$  

Multiple Choice

Which correctly shows

 $\sqrt{24}$  fully reduced?

•  $2\sqrt{6}$  

•  $4\sqrt{6}$  

•  $6\sqrt{2}$  

•  $2\sqrt{12}$  

Multiple Choice

Which of the following correctly shows the fully reduced form of

 $\sqrt{200}$  

•  $2\sqrt{10}$  

•  $10\sqrt{2}$  

•  $2\sqrt{50}$  

•  $14.14$  

Remember

• If the number under the root is a perfect square, the answer is just the square root

• Not all Roots Reduce

Multiple Choice

Reduce: √45

• 5√3
• 9√5
• 3√5
• 5√9

Multiple Choice

Reduce: √121

• √121
• 11
• 11√11
• 121

Multiple Choice

Reduce: √8

• 4
• 2
• 2√4
• 2√2

Multiple Choice

Reduce: √52

• 26
• 2√13
• 13√2
• 4√13

Multiple Choice

Reduce: √15

• 3√5
• √15
• 5√3
• 15

Multiple Choice

Reduce: √169

• 11
• 12
• 13
• 3√10

Multiple Choice

Reduce: √75

• 2√5
• 5√2
• 5√3
• 3√5

Multiple Choice

Reduce: √64

• 8
• 8√2
• 32
• 16

Multiple Choice

Reduce: √28

• 7√2
• 2√7
• 4√2
• 2√8

Multiple Choice

Reduce: 

 $\sqrt{32}$  

• 4√2

• √16

• 4

• 2√8

Multiple Choice

Reduce: 

 $\sqrt{18}$  

•  $9$  
  

•  $\sqrt{9}$  
  

•  $3\sqrt{2}$  
  

•  $2\sqrt{3}$