Chapter 8: Q. 50 (page 756)

In the following exercises, simplify using absolute values as necessary.
$ⓐ \sqrt{225 x^{2} y^{2} z^{2}} ⓑ \sqrt{36 r^{2} s^{20}} ⓒ \sqrt[3]{125 y^{18} z^{27}}$

Short Answer

Expert verified

Part(a) $\sqrt{225 x^{2} y^{2} z^{2}} = 15 |x y z|$

Part(b) $\sqrt{36 r^{2} s^{20}} = 6 |r| s^{10}$

Part(c) $\sqrt[3]{125 y^{18} z^{27}} = 5 y^{6} z^{9}$

Step by step solution

Part(a) Step 1. Given information

$ⓐ \sqrt{225 x^{2} y^{2} z^{2}}$

Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l} Since \\ \Rightarrow {(15 x y z)}^{2} = 225 x^{2} y^{2} z^{2} \\ \Rightarrow \sqrt[]{225 x^{2} y^{2} z^{2}} \\ \Rightarrow \sqrt{{(15 x y z)}^{2}} \\ \Rightarrow 15 |x y z| \end{array}$

Part(b) Step 1. Given information

$ⓑ \sqrt{36 r^{2} s^{20}}$

Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l} Since, \\ \Rightarrow {(6 r s^{10})}^{2} = 36 r^{2} s^{20} \\ \Rightarrow \sqrt[]{36 r^{2} s^{20}} \\ \Rightarrow \sqrt[]{{(6 r s^{10})}^{2}} \\ \Rightarrow 6 |r| s^{10} \end{array}$

Part(c) Step 1. Given information

$ⓒ \sqrt[3]{125 y^{18} z^{27}}$

Simplify using absolute values as necessary.

Step 2. Explanation

$\begin{array}{l} Since, \\ \Rightarrow {(5 y^{6} z^{9})}^{3} = 125 y^{18} z^{27} \\ \Rightarrow \sqrt[3]{125 y^{18} z^{27}} \\ \Rightarrow \sqrt[3]{{(5 y^{6} z^{9})}^{3}} \\ \Rightarrow 5 y^{6} z^{9} \end{array}$

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 values as necessary.
$ⓐ \sqrt{225 x^{2} y^{2} z^{2}} ⓑ \sqrt{36 r^{2} s^{20}} ⓒ \sqrt[3]{125 y^{18} z^{27}}$

Short Answer

Step by step solution

Part(a) Step 1. Given information

Step 2. Explanation

Part(b) Step 1. Given information

Step 2. Explanation

Part(c) Step 1. Given information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Pure Maths

Applied Mathematics

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify using absolute values as necessary.ⓐ225x2y2z2ⓑ36r2s20ⓒ125y18z273

Short Answer

Step by step solution

Part(a) Step 1. Given information

Step 2. Explanation

Part(b) Step 1. Given information

Step 2. Explanation

Part(c) Step 1. Given information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Pure Maths

Applied Mathematics

Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify using absolute values as necessary.
$ⓐ \sqrt{225 x^{2} y^{2} z^{2}} ⓑ \sqrt{36 r^{2} s^{20}} ⓒ \sqrt[3]{125 y^{18} z^{27}}$