Chapter 8: Q. 74 (page 743)

In the following exercises, simplify using absolute value signs as needed. $\sqrt{175 n^{13}}, \sqrt[5]{512 p^{5}}, \sqrt[4]{324 q^{7}}$

Short Answer

Expert verified

The expression on simplification is $5 n^{6} \sqrt{7 n}, 2 p \sqrt[5]{16}, | 3 q | \sqrt[4]{4 q^{3}}$ respectively

Step by step solution

Given information

Given the expression $\sqrt{175 n^{13}}, \sqrt[5]{512 p^{5}}, \sqrt[4]{324 q^{7}}$

Using the product property

Using the property, we get

$\sqrt{175 n^{13}} = \sqrt{25 n^{12} \cdot 7 n} \sqrt{175 n^{13}} = \sqrt{{(5 n^{6})}^{2} \cdot 7 n} \sqrt{175 n^{13}} = \sqrt{{(5 n^{6})}^{2}} \cdot \sqrt{7 n} \sqrt{175 n^{13}} = 5 |n^{6}| \sqrt{7 n} \sqrt{175 n^{13}} = 5 n^{6} \sqrt{7 n}$

Using the product property

Using the property, we get

$\sqrt[5]{512 p^{5}} = \sqrt[5]{32 p^{5} \cdot 16} \sqrt[5]{512 p^{5}} = \sqrt[5]{(2 p)^{5} \cdot 16} \sqrt[5]{512 p^{5}} = \sqrt[5]{(2 p)^{5}} \cdot \sqrt[5]{16} \sqrt[5]{512 p^{5}} = 2 p \sqrt[5]{16}$

Using the product property

Using the property, we have

$\sqrt[4]{324 q^{7}} = \sqrt[4]{81 q^{4} \cdot 4 q^{3}} \sqrt[4]{324 q^{7}} = \sqrt[4]{(3 q)^{4} \cdot 4 q^{3}} \sqrt[4]{324 q^{7}} = \sqrt[4]{(3 q)^{4}} \cdot \sqrt[4]{4 q^{3}} \sqrt[4]{324 q^{7}} = | 3 q | \sqrt[4]{4 q^{3}}$

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In the following exercises, simplify using absolute value signs as needed. $\sqrt{175 n^{13}}, \sqrt[5]{512 p^{5}}, \sqrt[4]{324 q^{7}}$

Short Answer

Step by step solution

Given information

Using the product property

Using the product property

Using the product property

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In the following exercises, simplify using absolute value signs as needed.175n13,512p55,324q74

Short Answer

Step by step solution

Given information

Using the product property

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

Geometry

Theoretical and Mathematical Physics

Pure Maths

Applied Mathematics

Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify using absolute value signs as needed. $\sqrt{175 n^{13}}, \sqrt[5]{512 p^{5}}, \sqrt[4]{324 q^{7}}$