Simplifying Radicals

Simplifying Radicals

By Molly Humphries

Simplifying Radicals

By Molly Humphries

​Now we will begin to simplify radicals

Before we start simplifying radicals, let's review perfect squares.

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.

Now, we are going to simplify radicals using prime factorization.

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

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

How to simplify a radical

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:

$$\sqrt{98}$$  

• $$7\sqrt{2}$$  

• $$2\sqrt{7}$$  

• $$49\sqrt{2}$$  

• $$2\sqrt{49}$$  

What if you have a number on the outside?

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 the following radical: √32

• 3√2
• 4√8
• 16√2
• 4√2

Multiple Choice

Simplify the following radical: √28

• 7√2
• 7√4
• 4√7
• 2√7

Multiple Choice

Simplify the following radical: √72

• 8√3
• 6√2
• 3√8
• 4√8

Multiple Choice

Simplify the following radical: √96

• 16√6
• 2√6
• 4√6
• √2

Multiple Choice

Simplify the following radical: √80

• 16√5
• 2√20
• 4√5
• 8√5

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

Simplify:

$$\sqrt{x^{15}}$$  

• $$x^{7.5}$$  

• $$x^{14}\sqrt{x}$$  

• $$x^7\sqrt{x}$$  

Multiple Choice

Simplify:

$$\sqrt{x^2y^7}$$  

• $$xy^3$$  

• $$xy^3\sqrt{y}$$  

• $$xy^3\sqrt{xy}$$  

Multiple Choice

Simplify:

$$\sqrt{80x^2y^4}$$  

• $$2xy^2\sqrt{20}$$  

• $$4xy^2\sqrt{5}$$