Chapter 11: Q. 73 (page 1069)

In the following exercises, simplify using absolute value signs as needed. $\sqrt{242 m^{23}}, \sqrt[4]{405 m^{10}}, \sqrt[5]{160 n^{8}}$

Short Answer

Expert verified

The expression on simplification is $11 |m^{11}| \sqrt{2 m}, 3 m^{2} \sqrt[4]{5 m^{2}}, 2 n \sqrt[5]{5 n^{3}}$ respectively

Step by step solution

Given information

Given the expression $\sqrt{242 m^{23}}, \sqrt[4]{405 m^{10}}, \sqrt[5]{160 n^{8}}$

Using the product property

Using the product property, we get

$\sqrt{242 m^{23}} = \sqrt{121 m^{22} \cdot 2 m} \sqrt{242 m^{23}} = \sqrt{121 m^{22}} \cdot \sqrt{2 m} \sqrt{242 m^{23}} = \sqrt{{(11 m^{11})}^{2}} \cdot \sqrt{2 m} \sqrt{242 m^{23}} = = 11 |m^{11}| \sqrt{2 m}$

Using the product property

Using the product property, we get

$\sqrt[4]{405 m^{10}} = \sqrt[4]{81 m^{8} \cdot 5 m^{2}} \sqrt[4]{405 m^{10}} = \sqrt[4]{81 m^{8}} \cdot \sqrt[4]{5 m^{2}} \sqrt[4]{405 m^{10}} = \sqrt[4]{{(3 m^{2})}^{4}} \cdot \sqrt[4]{5 m^{2}} \sqrt[4]{405 m^{10}} = |3 m^{2}| \sqrt[4]{5 m^{2}} \sqrt[4]{405 m^{10}} = 3 m^{2} \sqrt[4]{5 m^{2}}$

Using the product property

Using the property, we get

$\sqrt[5]{160 n^{8}} = \sqrt[5]{32 n^{5} \cdot 5 n^{3}} \sqrt[5]{160 n^{8}} = \sqrt[5]{32 n^{5}} \cdot \sqrt[5]{5 n^{3}} \sqrt[5]{160 n^{8}} = \sqrt[5]{(2 n)^{5}} \cdot \sqrt[5]{5 n^{3}} \sqrt[5]{160 n^{8}} = 2 n \sqrt[5]{5 n^{3}}$

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In the following exercises, simplify using absolute value signs as needed. $\sqrt{242 m^{23}}, \sqrt[4]{405 m^{10}}, \sqrt[5]{160 n^{8}}$

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.242m23,405m104,160n85

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

Probability and Statistics

Discrete Mathematics

Applied Mathematics

Statistics

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify using absolute value signs as needed. $\sqrt{242 m^{23}}, \sqrt[4]{405 m^{10}}, \sqrt[5]{160 n^{8}}$