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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 462. (page 1124)

Simplify:
(a) $\sqrt[3]{r^{5}}$
(b)role="math" localid="1650580893666" $\sqrt[4]{s^{10}}$

Short Answer

Expert verified

(a) $\sqrt[3]{r^{5}} = = r \sqrt[3]{r^{2}}$

(b) $\sqrt[4]{s^{10}} = s^{2} \sqrt[4]{s^{2}}$

Step by step solution

01

Part (a) Step 1: Given Information

The given expression is $\sqrt[3]{r^{5}}$ .

02

Part (a) Step 2: Simplification

Rewrite as product using largest perfect cube factor.

$\sqrt[3]{r^{3} r^{2}}$

Write as product of two radicals

role="math" localid="1650580858286" $= \sqrt[3]{r^{3}} \sqrt[3]{r^{2}}$

Simplify

$= r \sqrt[3]{r^{2}}$

03

Part (b) Step 1: Given Information

The given expression is $\sqrt[4]{s^{10}}$

04

Part (b) Step 2: Simplification

Rewrite radicand as product using greatest perfect fourth power factor

$\sqrt[4]{s^{8} s^{2}}$

Rewrite using product of two radicands

$= \sqrt[4]{s^{8}} \sqrt[4]{s^{2}}$

Simplify

$= s^{2} \sqrt[4]{s^{2}}$

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Most popular questions from this chapter

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A helicopter dropped a rescue package from a height of $1, 296$ feet. Use the formula role="math" localid="1647883430342" $t = \frac{\sqrt{h}}{4}$ to find how many seconds it took for the package to reach the ground.

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Part (a): Is $x = - 2$ a solution?

Part (b): Is $x = 1$ a solution?

In the following exercises, solve:

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