Roots & Radical Expressions

Roots & Radical Expressions

​Dr. Tom Giles

​Roots & Radical Expressions Primary Objectives

​Roots & Radical Expressions Primary Objectives

Multiple Choice

(3x)^1/2

• √3x
• 3√x
• 3x
• √3

Multiple Choice

• A
• B
• C
• D

Multiple Choice

• y
• y²
• √y
• y√0

Multiple Choice

Multiple Choice

Re-write the expression in radical form.
x^2/3

• (∛x)²
• √x³
• (1/x)
• ∛x

Multiple Choice

$$\sqrt{45}$$  =

• $$3\sqrt{5}$$  

• $$5\sqrt{3}$$  

• $$9\sqrt{5}$$  

• $$5\sqrt{9}$$  

Multiple Choice

$$\sqrt{147}$$  

• $$3\sqrt{49}$$  

• $$6\sqrt{3}$$  

• $$7\sqrt{3}$$  

• $$9\sqrt{7}$$  

Multiple Choice

$$\sqrt{112}$$  

• $$4\sqrt{7}$$  

• $$16\sqrt{3}$$  

• $$16\sqrt{7}$$  

• $$4\sqrt{3}$$  

Multiple Select

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

• 38

• 48

• 144

• 256

Fill in the Blank

Is 400 a Perfect Square?

Multiple Choice

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

• Yes

• No

• I have no idea

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

$$\sqrt{200}$$  

• $$2\sqrt{10}$$  

• $$10\sqrt{2}$$  

• $$2\sqrt{50}$$  

• $$14.14$$  

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: 

$$\sqrt{18}$$  

• $$9$$  
  

• $$\sqrt{9}$$  
  

• $$3\sqrt{2}$$  
  

• $$2\sqrt{3}$$  
  

Multiple Choice

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

• Yes

• No

• I have no idea

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

$$\sqrt{200}$$  

• $$2\sqrt{10}$$  

• $$10\sqrt{2}$$  

• $$2\sqrt{50}$$  

• $$14.14$$  

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: 

$$\sqrt{18}$$  

• $$9$$  
  

• $$\sqrt{9}$$  
  

• $$3\sqrt{2}$$  
  

• $$2\sqrt{3}$$  
  

Multiple Choice

$$2\sqrt{150}+3\sqrt{175}+4\sqrt{24}$$  

• $$2\sqrt{6}+15\sqrt{7}$$  

• $$18\sqrt{6}+15\sqrt{7}$$  

• $$17\sqrt{13}$$  

Multiple Choice

2√5 + 4√5 =

• 6√10
• 8√10
• 8√5
• 6√5

Multiple Choice

Simplify
 
2√27+3√3

• 15√30
• 5√3
• 9√3
• 9√8

Multiple Choice

Simplify 
-2√2 - 3√8 - √5

•  -8√2-√5
• -8√2-√9
• -14√3-√7
• -2√4-√3

Multiple Choice

Simplify
3√2 - 3√18

•  -4√8
• 4√9-6√3
• 5√12
• -6√2

Multiple Choice

√5 + √20

• 5
• 25
• 3√5
• 2√3

Multiple Choice

√18 - √12

• √6

• 2√3

• $$3\sqrt{2}-2\sqrt{3}$$
  

• √5