Chapter 8: Q. 64 (page 771)

In the following exercises, use the Product Property to simplify radical expressions a. $\sqrt[3]{625}$ , b. $\sqrt[6]{128}$

Short Answer

Expert verified

The expression in simplified form is $5 \sqrt[3]{5}, 2 \sqrt[6]{2}$ respectively

Step by step solution

Given information

Given the expression $\sqrt[3]{625}, \sqrt[6]{128}$

Using the product property to simplify

Using the property, we get

$\sqrt[3]{625} = \sqrt[3]{125 \cdot 5} \sqrt[3]{625} = \sqrt[5]{125} \times \sqrt[3]{5} \sqrt[3]{625} = \sqrt[3]{5^{3}} \times \sqrt[3]{5} \sqrt[3]{625} = 5 \sqrt[3]{5}$

Checking for another expression

Using the property, we get

$\sqrt[6]{128} = \sqrt[6]{64 \times 2} \sqrt[6]{128} = \sqrt[6]{64} \times \sqrt[6]{2} \sqrt[6]{128} = \sqrt[6]{2^{6}} \times \sqrt[6]{2} \sqrt[6]{128} = 2 \sqrt[6]{2}$

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In the following exercises, use the Product Property to simplify radical expressions a. $\sqrt[3]{625}$ , b. $\sqrt[6]{128}$

Short Answer

Step by step solution

Given information

Using the product property to simplify

Checking for another expression

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In the following exercises, use the Product Property to simplify radical expressions a. 6253, b.1286

Short Answer

Step by step solution

Given information

Using the product property to simplify

Checking for another expression

One App. One Place for Learning.

Most popular questions from this chapter

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In the following exercises, use the Product Property to simplify radical expressions a. $\sqrt[3]{625}$ , b. $\sqrt[6]{128}$