Radical Expressions

Radical Expressions​

By MS. BOULIGNY

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Lesson 20-1 Objectives:

I can write and simplify radical expressions. I can understand what is meant by a rational exponent.​

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Lesson 20-1 Standards:

HSN-RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

HSA-SSE.A.2​ Use the structure of a an expression to identify ways to rewrite it .

Multiple Choice

A square rug has an area of 36 square feet.

What is the length of a side of the rug?

• 6 feet

• 36 feet

• 12 feet

• 9 feet

Poll

How familiar are you with radical expressions?

• Very!

• Somewhat.

• What is that?

• I've seen it, but don't know how to solve.

Vocabulary

Radical Expressions | 4 minutes

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Multiple Choice

Examine the following radical expression. What is the index?

$$\sqrt[5]{108}$$  

• 5

• 108

• 36

Multiple Choice

Examine the following radical expression. What is the radicand?

$$\sqrt[5]{108}$$  

• 3

• 108

• 36

How to find the root of a number or expression

• Finding the square root of a number or expression is the inverse operation of squaring a number or expression.​

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Multiple Choice

Evaluate: $$\sqrt[]{81}$$  

• 9

• 8

• 81

• 2

Multiple Choice

Evaluate: $$\sqrt[3]{8}$$  

• 3

• 8

• 2

• 4

Multiple Choice

Evaluate: $$\sqrt[3]{125}$$  

• 5

• 25

• 3

Simplifying radical Expressions

1. Find the largest perfect square that is a factor of the number

2. Write the factor pair under the square root

3. Separate into two square roots.

4. We choose a perect square because we know its square root is an integer.

5. Imply multiplication​

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Multiple Choice

Examine the radical expression. Which question best represents this expression?

$$\sqrt[5]{108}$$  

• What value can be multiplied by itself 108 times to obtain 5?

• What value can be multiplied by itself 5 times to obtain 108?

• What is the value of 108 divided by 5?

• What is the value of 5 divided by 108?

Multiple Choice

Evaluate: $$\sqrt[]{75}$$  

• $$\sqrt[]{25\cdot3}$$  

• $$\sqrt[5]{3}$$  

• $$\sqrt[]{5\cdot3}$$  

• $$\sqrt[3]{5}$$  

Multiple Choice

Write as a radical expression: $$13\ \frac{1}{4}$$  

• $$\sqrt[13]{4}$$  

• $$\sqrt[1]{13}$$  

• $$\sqrt[4]{13}$$  

Exit Ticket

Multiple Choice

Evaluate: $$\sqrt[]{16}$$  

• 8

• 4

• 6

• 2

Multiple Choice

Evaluate: $$\sqrt[]{72}$$  

• $$\sqrt[]{36\cdot2}$$  

• $$\sqrt[2]{6}$$  

• $$\sqrt[6]{2}$$  

• $$\sqrt[]{9\cdot4\cdot2}$$  

Multiple Choice

Write as a radical expression: $$7\ \frac{1}{5}$$  

• $$\sqrt[7]{5}$$  

• $$\sqrt[5]{7}$$  

• $$\sqrt[1]{7}$$  

Poll

How do you feel about radical expressions?

• Comfortable

• Need more practice

• Amazing!

• Confused