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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. 47 (page 756)

In the following exercises, simplify using absolute values as necessary.
$鈸� \sqrt{144 x^{2} y^{2}} 鈸� \sqrt{169 w^{8} y^{10}} 鈸� \sqrt[3]{8 a^{51} b^{6}}$

Short Answer

Expert verified

Part(a) $\sqrt{144 x^{2} y^{2}} = 12 |x y|$

Part(b) $\sqrt{169 w^{8} y^{10}} = 13 w^{4} |y^{5}|$

Part(c)role="math" localid="1645460705391" $\sqrt[3]{8 a^{51} b^{6}} = 2 a^{17} b^{2}$

Step by step solution

01

Part(a) Step 1. Given information

$鈸� \sqrt{144 x^{2} y^{2}}$

Simplify using absolute values as necessary.

02

Step 2. Explanation

$\begin{array}{l} Since \\ {(12 x y)}^{2} = 144 x^{2} y^{2} \\ 鈬� \sqrt[]{144 x^{2} y^{2}} \\ 鈬� \sqrt{{(12 x y)}^{2}} \\ 鈬� 12 |x y| \end{array}$

03

Part(b) Step 1. Given information

$鈸� \sqrt{169 w^{8} y^{10}}$

Simplify using absolute values as necessary.

04

Step 2. Explanation

$\begin{array}{l} Since, \\ 鈬� {(13 w^{4} y^{5})}^{2} = 169 w^{8} y^{10} \\ 鈬� \sqrt[]{169 w^{8} y^{10}} \\ 鈬� \sqrt[]{{(13 w^{4} y^{5})}^{2}} \\ 鈬� 13 w^{4} |y^{5}| \end{array}$

05

Part(c) Step 1. Given information

$鈸� \sqrt[3]{8 a^{51} b^{6}}$

Simplify using absolute values as necessary.

06

Step 2. Explanation

$\begin{array}{l} Since, \\ 鈬� {(2 a^{17} b^{2})}^{3} 鈬� = 8 a^{51} b^{6} \\ 鈬� \sqrt[3]{8 a^{51} b^{6}} \\ 鈬� \sqrt[3]{{(2 a^{17} b^{2})}^{3}} \\ 鈬� 2 a^{17} b^{2} \end{array}$

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Most popular questions from this chapter

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{45 r^{3}}{s^{10}}}$

(b) $\sqrt[3]{\frac{625 u^{10}}{v^{3}}}$

(c) $\sqrt[4]{\frac{729 c^{21}}{d^{8}}}$

In the following exercises, simplify using absolute value signs as needed. $\sqrt{80 s^{15}}, \sqrt[5]{96 a^{7}}, \sqrt[6]{128 b^{7}}$

Use the Quotient Property to simplify square roots.

$\sqrt{\frac{98 r^{5}}{100}}$

In the following exercises, solve.
$\sqrt{v - 10} + 10 = v$

In the following exercises, solve.

$\sqrt{5 x - 6} = 8$

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