Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.4 - Adding and Subtracting Radical Expressions - 7.4 Exercises: 35

Answer

$-m^2p\sqrt[4]{mp^2}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $ 2\sqrt[4]{m^9p^6}-3m^2p\sqrt[4]{mp^2} ,$ simplify first each term by expressing the radicand as a factor that is a perfect power of the index. Then, extract the root. Finally, combine the like radicals. $\bf{\text{Solution Details:}}$ Expressing the radicand as an expression that contains a factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 2\sqrt[4]{m^8p^2\cdot mp^2}-3m^2p\sqrt[4]{mp^2} \\\\= 2\sqrt[4]{(m^2p)^4\cdot mp^2}-3m^2p\sqrt[4]{mp^2} .\end{array} Extracting the roots of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 2m^2p\sqrt[4]{mp^2}-3m^2p\sqrt[4]{mp^2} .\end{array} By combining like radicals, the expression above is equivalent to \begin{array}{l}\require{cancel} (2m^2p-3m^2p)\sqrt[4]{mp^2} \\\\= -m^2p\sqrt[4]{mp^2} .\end{array}
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.