Q. 73 In the following exercises, simp... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

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

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

Using the product property

Using the product property, we get

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

Using the product property

Using the property, we get

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

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Calculus

Applied Mathematics

Theoretical and Mathematical Physics

Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

91影视

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

Mechanics Maths

Calculus

Applied Mathematics

Theoretical and Mathematical Physics

Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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