Chapter 8: Q. 71 (page 771)

In the following exercises, simplify using absolute value signs as needed. $\sqrt{125 r^{13}}, \sqrt[3]{108 x^{5}}, \sqrt[4]{48 y^{6}}$

Short Answer

Expert verified

The expression in simplified form is $5 r^{6} \sqrt{5 r}, 3 x \sqrt[3]{4 x^{2}}, 2 | y | \sqrt[4]{3 y^{2}}$ respectively

Step by step solution

Given information

Given the expression

Using the product property

Using the property, we get

$\sqrt{125 r^{13}} = \sqrt{25 r^{12} \cdot 5 r^{1}} \sqrt{125 r^{13}} = \sqrt{{(5 r^{6})}^{2} \cdot 5 r} \sqrt{125 r^{13}} = \sqrt{{(5 r^{6})}^{2}} \cdot \sqrt{5 r} \sqrt{125 r^{13}} = 5 |r^{6}| \sqrt{5 r} \sqrt{125 r^{13}} = 5 r^{6} \sqrt{5 r}$

Using the product property

Using the property, we get

$\sqrt[3]{108 x^{5}} = \sqrt[3]{27 x^{3} \cdot 4 x^{2}} \sqrt[3]{108 x^{5}} = \sqrt[3]{(3 x)^{3}} \cdot \sqrt[3]{4 x^{2}} \sqrt[3]{108 x^{5}} = 3 x \sqrt[3]{4 x^{2}}$

Using the property

Using the property, we get

$\sqrt[4]{48 y^{6}} = \sqrt[4]{16 y^{4} \cdot 3 y^{2}} \sqrt[4]{48 y^{6}} = \sqrt[4]{16 y^{4} \cdot 3 y^{2}} \sqrt[4]{48 y^{6}} = \sqrt[4]{(2 y)^{4}} \cdot \sqrt[4]{3 y^{2}} \sqrt[4]{48 y^{6}} = 2 | y | \sqrt[4]{3 y^{2}}$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, simplify using absolute value signs as needed. $\sqrt{125 r^{13}}, \sqrt[3]{108 x^{5}}, \sqrt[4]{48 y^{6}}$

Short Answer

Step by step solution

Given information

Using the product property

Using the product property

Using the property

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify using absolute value signs as needed.125r13,108x53,48y64

Short Answer

Step by step solution

Given information

Using the product property

Using the product property

Using the property

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify using absolute value signs as needed. $\sqrt{125 r^{13}}, \sqrt[3]{108 x^{5}}, \sqrt[4]{48 y^{6}}$