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: 29

Answer

$(3-4x)\sqrt[3]{xy^2}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $ 3\sqrt[3]{xy^2}-2\sqrt[3]{8x^4y^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} 3\sqrt[3]{xy^2}-2\sqrt[3]{8x^3\cdot xy^2} \\\\= 3\sqrt[3]{xy^2}-2\sqrt[3]{(2x)^3\cdot xy^2} .\end{array} Extracting the roots of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 3\sqrt[3]{xy^2}-2(2x)\sqrt[3]{xy^2} \\\\= 3\sqrt[3]{xy^2}-4x\sqrt[3]{xy^2} .\end{array} By combining like radicals, the expression above is equivalent to \begin{array}{l}\require{cancel} (3-4x)\sqrt[3]{xy^2} .\end{array}
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