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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. 42 (page 756)

In the following exercise, simplify using absolute values as necessary.
$鈸� \sqrt{81 x^{36}} 鈸� - \sqrt{25 x^{2}}$

Short Answer

Expert verified

Part(a) $\sqrt{81 x^{36}} = 9 x^{18}$

Part(b) $鈭� \sqrt{25 x^{2}} = - 5 |x|$

Step by step solution

01

Part(a) Step 1. Given information

$鈸� \sqrt{81 x^{36}}$

In the following exercise, simplify using absolute values as necessary.

02

Step 2. Explanation

$\begin{array}{l} Since; \\ = 81 x^{36} \\ 鈬� \sqrt{81 x^{36}} \\ 鈬� \sqrt{{(9 x^{18})}^{2}} \\ 鈬� 9 x^{18} \\ Sincetheindexniseven= \sqrt[n]{a^{n}} = |n| \\ 鈬� \sqrt{81 x^{36}} = 9 x^{18} \end{array}$

03

Part(b) Step 1. Given information

$鈸� - \sqrt{25 x^{2}}$

In the following exercise, simplify using absolute values as necessary.

04

Explanation

$\begin{array}{l} Since; \\ 鈬� = 25 x^{2} \\ 鈬� 鈭� \sqrt{25 x^{2}} \\ 鈬� - 5 x^{2} \\ Sincetheindexniseven= \sqrt[n]{a^{n}} = |n| \\ 鈬� 鈭� \sqrt{25 x^{2}} = - 5 |x| \end{array}$

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