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: 37

Answer

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

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $ \sqrt[3]{64xy^2}+\sqrt[3]{27x^4y^5} ,$ 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} \sqrt[3]{64\cdot xy^2}+\sqrt[3]{27x^3y^3\cdot xy^2} \\\\= \sqrt[3]{(4)^3\cdot xy^2}+\sqrt[3]{(3xy)^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} 4\sqrt[3]{xy^2}+3xy\sqrt[3]{xy^2} .\end{array} By combining like radicals, the expression above is equivalent to \begin{array}{l}\require{cancel} (4+3xy)\sqrt[3]{xy^2} .\end{array}
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