Simplifying Radicals

Simplifying Radicals - Get out your calculator.

The product of a number, multiplied by itself.

​Perfect Squares

The product of a number multiplied by itself 3 times.

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​Perfect Cubes

​Square Root

Simplifying Using Factor Tree

​Steps

1. Use factor tree to simplify as much as possible.

2. For every pair of numbers, 1 is pulled out.

3. If a number does not have a pair it stays under the radical.

4. If multiple numbers are pulled out or stay in, then you will multiply those numbers​

Draw

Simplify $$\sqrt[]{72}$$

Draw

SImplify $$\sqrt[]{12}$$  

Multiple Choice

• √12
• 12
• 72
• √72

Multiple Choice

• √8
• 4
• √4
• 8

Multiple Choice

√48

• 4√2
• 6√3
• 4√3
• 4√2

Multiple Choice

√96

• 4√6
• 3√6
• 6√5
• 6√8

​Cube roots

​The opposite of cubing a number.

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​Think ____ x ____ x ____ (all the same number) = 64

Multiple Choice

$$\sqrt[3]{27}$$  

• 3

• 9

• 24

Simplifying Using Factor Tree - Cube Roots

​Steps

1. Use factor tree to simplify as much as possible.

2. For every set of 3 numbers, 1 is pulled out.

3. If a number does not have a set of 3 it stays under the radical.

4. If multiple numbers are pulled out or stay in, then you will multiply those numbers​

Draw

Simplify $$\sqrt[3]{56}$$

Draw

Simplify $$\sqrt[3]{40}$$

Multiple Choice

Simplify ∛64

• 4

• 8

• 2∛2

• 4∛2

Multiple Choice

Simplify ∛32

• 4

• 2∛4

• 4∛2

• 8