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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. 50 (page 756)

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

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

01

Part(a) Step 1. Given information

$鈸� \sqrt{225 x^{2} y^{2} z^{2}}$

Simplify using absolute values as necessary.

02

Step 2. Explanation

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

03

Part(b) Step 1. Given information

$鈸� \sqrt{36 r^{2} s^{20}}$

Simplify using absolute values as necessary.

04

Step 2. Explanation

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

05

Part(c) Step 1. Given information

$鈸� \sqrt[3]{125 y^{18} z^{27}}$

Simplify using absolute values as necessary.

06

Step 2. Explanation

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

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