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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 41 (page 756)

In the following exercises, simplify using absolute values as necessary
$鈸� \sqrt{121 m^{20}} 鈸� - \sqrt{64 a^{2}}$

Short Answer

Expert verified

Part(a) $\sqrt[]{121 m^{20}} = 11 m^{10}$

Part(b) $鈭� \sqrt[]{64 a^{2}} = 鈭� 8 |a|$

Step by step solution

01

Part(a) Step 1. Given information

$鈸� \sqrt{121 m^{20}}$

Simplify using absolute values as necessary.

02

Step 2. Explanation

$\begin{array}{l} Since \\ 鈬� {(11 (m^{10}))}^{2} = {121m}^{20} \\ 鈬� \sqrt[]{121 m^{20}} \\ 鈬� \sqrt[]{{(11 (m^{10}))}^{2}} \\ Sincetheindexniseven= \sqrt[n]{a^{n}} = |a| . \\ {Sincem}^{10} {ispositive,wedonotneedanm}^{10} absolutevaluesign. \\ 鈬� \sqrt[]{121 m^{20}} = 11 m^{10} \end{array}$

03

Part(b) Step 1. Given information

$鈸� - \sqrt{64 a^{2}}$

Simplify using absolute values as necessary.

04

Step 2. Explanation

$\begin{array}{l} Since \\ 鈬� {(8 a)}^{2} = {64a}^{2} \\ 鈬� 鈭� \sqrt[]{64 a^{2}} \\ 鈬� \sqrt[]{{(8 a)}^{2}} \\ Sincetheindexniseven= \sqrt[n]{a^{n}} = |a| . \\ 鈬� 鈭� \sqrt[]{64 a^{2}} = 鈭� 8 |a| \end{array}$

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Most popular questions from this chapter

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