Simplifying Radicals

Examples

How to simplify a radical

What if you have a number on the outside?

What if you have variables?

1. Make sure the variable is an even power
2. If it's not even, subtract one from the exponent and rewrite as a product
3. Take the variable with the even power and divide by 2 - put that on the outside of the radical

Multiple Choice

$$\sqrt{15}=\sqrt{5}\cdot\sqrt{3}$$  True or False?

• True

• False

Multiple Choice

$$\sqrt{50}=25\sqrt{2}$$  True or False?

• True

• False

Multiple Choice

Simplify

$$\sqrt{24}$$  

• $$4\sqrt{6}$$  

• $$2\sqrt{6}$$  

• $$6\sqrt{2}$$  

• $$6\sqrt{4}$$  

Multiple Choice

√28

• 7√2

• 7√4

• 4√7

• 2√7

Multiple Choice

√45

• 3√5

• 5√3

• 9√5

• 5√9

Multiple Choice

√96

• 16√6

• 2√6

• 4√6

• √2

Multiple Choice

√125

• 5√5

• 25√5

• 5√25

• 5√2

Multiple Choice

√216

• 6√4

• 4√6

• 36√6

• 6√6

Multiple Choice

What is the largest perfect square that you use to simplify

$$\sqrt{24}$$  

• 1

• 4

• 9

• 16

Multiple Choice

Simplify

$$\sqrt{24}$$  

• $$4\sqrt{6}$$  

• $$2\sqrt{6}$$  

• $$6\sqrt{2}$$  

• $$6\sqrt{4}$$  

Multiple Choice

Simplify:

$$\sqrt{98}$$  

• $$7\sqrt{2}$$  

• $$2\sqrt{7}$$  

• $$49\sqrt{2}$$  

• $$2\sqrt{49}$$  

Multiple Choice

Simplify:

$$10\sqrt{96}$$  

• $$40\sqrt{6}$$  

• $$160\sqrt{6}$$  

• $$96\sqrt{10}$$  

• $$60\sqrt{16}$$  

Multiple Choice

Simplify:

$$3\sqrt{125}$$  

• $$75\sqrt{3}$$  

• $$8\sqrt{5}$$  

• $$15\sqrt{5}$$  

• $$15\sqrt{25}$$  

Multiple Choice

Simplify:

$$\sqrt{x^{15}}$$  

• $$x^{7.5}$$  

• $$x^{14}\sqrt{x}$$  

• $$x^7\sqrt{x}$$  

Multiple Choice

Which of the following is a perfect square?

• 12
• 90
• 40
• 64

Multiple Choice

Which of the following in NOT a perfect square?

• 49

• 81

• 111

• 144

Multiple Choice

144

• is a perfect square.

• is not a perfect square.

Multiple Choice

65

• Is a perfect square.
• Is not a perfect square.

Multiple Choice

169

• Is a perfect square.
• Is not a perfect square.

Multiple Choice

Use a factor tree to find the prime factorization of 60

• 5 x 3 x 2 x 2

• 7 x 6 x 5

Multiple Choice

Use a factor tree to find the prime factorization of 72

• 2 x 2 x 2 x 3 x 3

• 4 x 3 x 3 x 2

Multiple Choice

Use a factor tree to find the prime factorization of 32

• 2 x 2 x 2 x 4

• 2 x 2 x 2 x 2 x 2

Multiple Choice

Simplify the following radical: √80

• 16√5
• 2√20
• 4√5
• 8√5

Multiple Choice

Simplify the following radical: √96

• 16√6
• 2√6
• 4√6
• √2

Multiple Choice

Simplify the following radical: √72

• 8√3
• 6√2
• 3√8
• 4√8