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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q 635. (page 1149)

In the following exercises, simplify.
$\sqrt{108 r^{5} s^{3}}$

Short Answer

Expert verified

The simplification of $\sqrt{108 r^{5} s^{3}}$ is, $6 r^{2} s \sqrt{3 r s}$ .

Step by step solution

01

Step1. Given information

Given expression is $\sqrt{108 r^{5} s^{3}}$ .

02

Step2. Rewrite the radicand as a product using the largest perfect square factor.

$\sqrt{108 r^{5} s^{3}} = \sqrt{36 r^{4} s^{2} . 3 r s}$

03

Step3. Rewrite the radical as the product of two radicals.

$\sqrt{36 r^{4} s^{2} . 3 r s} = \sqrt{36 r^{4} s^{2}} \sqrt{3 r s}$

04

Step4. Simplification

$\sqrt{36 r^{4} s^{2}} \sqrt{3 r s} = 6 r^{2} s \sqrt{3 r s}$

05

Step5. Check

$\sqrt{108 r^{5} s^{3}} = \sqrt{36 r^{4} s^{2} . 3 r s} = \sqrt{36 r^{4} s^{2} 3 r s} = \sqrt{36 r^{4} s^{2}} \sqrt{3 r s} = 6 r^{2} s \sqrt{3 r s}$

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