Chapter 8: Q. 70 (page 771)

In the following exercises, simplify using absolute value signs as needed. $\sqrt{r^{25}}, \sqrt[5]{p^{8}}, \sqrt[4]{m^{5}}$

Short Answer

Expert verified

The expression in simplified form is $r^{12} \sqrt{r}, p \sqrt[5]{p^{3}}, | m | \sqrt[4]{m}$ respectively

Step by step solution

Given information

Given the expression $\sqrt{r^{25}}, \sqrt[5]{p^{8}}, \sqrt[4]{m^{5}}$

Using the product property

Using the product property, we get

$\sqrt{r^{25}} = \sqrt{{(r^{12})}^{2} \cdot r^{1}} \sqrt{r^{25}} = \sqrt{{(r^{12})}^{2} \cdot r} \sqrt{r^{25}} = \sqrt{{(r^{12})}^{2}} \cdot \sqrt{r} \sqrt{r^{25}} = |r^{12}| \sqrt{r} \sqrt{r^{25}} = r^{12} \sqrt{r}$

Step 3; Using the product property

Using the property, we get

$\sqrt[5]{p^{8}} = \sqrt[5]{p^{5} \cdot p^{3}} \sqrt[5]{p^{8}} = = \sqrt[5]{p^{5}} \cdot \sqrt[5]{p^{3}} \sqrt[5]{p^{8}} = p \sqrt[5]{p^{3}}$

Using the product property

Using the property, we get

$\sqrt[4]{m^{5}} = \sqrt[4]{{(m^{1})}^{4} \cdot m^{1}} \sqrt[4]{m^{5}} = \sqrt[4]{{(m^{1})}^{4} \cdot m} \sqrt[4]{m^{5}} = \sqrt[4]{{(m^{1})}^{4}} \cdot \sqrt[4]{m} \sqrt[4]{m^{5}} = | m | \sqrt[4]{m}$

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In the following exercises, simplify using absolute value signs as needed. $\sqrt{r^{25}}, \sqrt[5]{p^{8}}, \sqrt[4]{m^{5}}$

Short Answer

Step by step solution

Given information

Using the product property

Step 3; Using the product property

Using the product property

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In the following exercises, simplify using absolute value signs as needed.r25,p85,m54

Short Answer

Step by step solution

Given information

Using the product property

Step 3; Using the product property

Using the product property

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

In the following exercises, simplify using absolute value signs as needed. $\sqrt{r^{25}}, \sqrt[5]{p^{8}}, \sqrt[4]{m^{5}}$