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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. 49 (page 756)

In the following exercises, simplify using absolute values as necessary.
$鈸� \sqrt{121 a^{2} b^{2}} 鈸� \sqrt{9 c^{8} d^{12}} 鈸� \sqrt[3]{64 x^{15} y^{66}}$

Short Answer

Expert verified

Part(a) $\sqrt{121 a^{2} b^{2}} = 11 |a b|$

Part(b) $\sqrt{9 c^{8} d^{12}} = 3 c^{4} d^{6}$

Part(c) $\sqrt[3]{64 x^{15} y^{66}} = 4 x^{5} y^{22}$

Step by step solution

01

Part(a) Step 1. Given information

$鈸� \sqrt{121 a^{2} b^{2}}$

Simplify using absolute values as necessary.

02

Step 2. Explanation

$\begin{array}{l} Since \\ 鈬� {(11 a b)}^{2} = 121 a^{2} b^{2} \\ 鈬� \sqrt[]{121 a^{2} b^{2}} \\ 鈬� \sqrt{{(11 a b)}^{2}} \\ 鈬� 11 |a b| \end{array}$

03

Part(b) Step 1. Given information

$鈸� \sqrt{9 c^{8} d^{12}}$

Simplify using absolute values as necessary.

04

Step 2. Explanation

$\begin{array}{l} Since, \\ 鈬� {(3 c^{4} d^{6})}^{2} = 9 c^{8} d^{12} \\ 鈬� \sqrt[]{9 c^{8} d^{12}} \\ 鈬� \sqrt[]{{(3 c^{4} d^{6})}^{2}} \\ 鈬� 3 c^{4} d^{6} \end{array}$

05

Part(c) Step 1. Given information

$鈸� \sqrt[3]{64 x^{15} y^{66}}$

Simplify using absolute values as necessary.

06

Step 2. Explanation

$\begin{array}{l} Since, \\ 鈬� {(4 x^{5} y^{22})}^{3} = 64 x^{15} y^{66} \\ 鈬� \sqrt[3]{64 x^{15} y^{66}} \\ 鈬� \sqrt[3]{{(4 x^{5} y^{22})}^{3}} \\ 鈬� 4 x^{5} y^{22} \end{array}$

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Most popular questions from this chapter

In the following exercises, solve.
$\sqrt{12 u + 1} - 11 = 0$

Explain how you know that

$\sqrt[5]{x^{10}} = x^{2}$

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{50 r^{5} s^{2}}{128 r^{2} s^{6}}}$

(b) $\sqrt[3]{\frac{24 m^{9} n^{7}}{375 m^{4} n}}$

(c) $\sqrt[4]{\frac{81 m^{2} n^{8}}{256 m n^{2}}}$

In the following exercises, simplify using absolute value signs as needed.

$\sqrt{y^{11}} \sqrt[3]{r^{5}} \sqrt[4]{s^{10}}$

Explain why $7 + \sqrt{9}$ is not equal to $\sqrt{7 + 9}$ .

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