Simplify Radicals and Operations with Radicals

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

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