College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.7 - Radical Expressions - R.7 Exercises - Page 68: 60

Answer

$\dfrac{\sqrt[3]{36p^2}}{4p^2} $

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $ \sqrt[3]{\dfrac{9}{16p^4}} ,$ make the denominator a perfect power of the index so that the final result will already be in rationalized form. Then find a factor of the radicand that is a perfect power of the index. Finally, extract the root of that factor. $\bf{\text{Solution Details:}}$ Multiplying the radicand that will make the denominator a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt[3]{\dfrac{9}{16p^4}\cdot\dfrac{4p^2}{4p^2}} \\\\= \sqrt[3]{\dfrac{36p^2}{64p^6}} .\end{array} Factoring the radicand into an expression that is a perfect power of the index and then extracting its root result to \begin{array}{l}\require{cancel} \sqrt[3]{\dfrac{1}{64p^6}\cdot36p^2} \\\\= \sqrt[3]{\left(\dfrac{1}{4p^2}\right)^3\cdot36p^2} \\\\= \dfrac{1}{4p^2}\sqrt[3]{36p^2} \\\\= \dfrac{\sqrt[3]{36p^2}}{4p^2} .\end{array} Note that all variables are assumed to have positive values.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.