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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. 8.23 (page 754)

Simplify: $(a) \sqrt{100 a^{2} b^{2}} (b) \sqrt{144 p^{12} q^{20}} (c) \sqrt[3]{8 x^{30} y^{12}}$

Short Answer

Expert verified

The solutions of (a), (b) and (c) are $10 |a b|, 12 p^{6} q^{10} a n d 2 x^{10} y^{4}$ respectively.

Step by step solution

01

Part (a) Step 1. Given information

The root: $\sqrt{100 a^{2} b^{2}}$

02

Part (a) Step 2. Calculation

We have,

$\sqrt{100 a^{2} b^{2}} = \sqrt{{(10 a b)}^{2}} \sin c e {(10 a b)}^{2} = 100 a^{2} b^{2} = 10 |a b|$

Therefore, the solution is $10 |a b|$

03

Part (b) Step 1. Given information

The root: $\sqrt{144 p^{12} q^{20}}$

04

Part (b) Step 2. Calculation

We have,

$\sqrt{144 p^{12} q^{20}} = \sqrt{{(12 p^{6} q^{10})}^{2}} \sin c e {(12 p^{6} q^{10})}^{2} = 144 p^{12} q^{20} = 12 p^{6} q^{10}$

Therefore, the solution is $12 p^{6} q^{10}$

05

Part (c) Step 1. Given information

The root: $\sqrt[3]{8 x^{30} y^{12}}$

06

Part (c) Step 2. Calculation

We have,

$\sqrt[3]{8 x^{30} y^{12}} = \sqrt[3]{{(2 x^{10} y^{4})}^{3}} \sin c e {(2 x^{10} y^{4})}^{3} = 8 x^{30} y^{12} = 2 x^{10} y^{4}$

Therefore, the solution is $2 x^{10} y^{4}$

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