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: 24

Answer

$53\sqrt[3]{3}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $ 15\sqrt[3]{81}+4\sqrt[3]{24} ,$ 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} 15\sqrt[3]{27\cdot3}+4\sqrt[3]{8\cdot3} \\\\= 15\sqrt[3]{(3)^3\cdot3}+4\sqrt[3]{(2)^3\cdot3} .\end{array} Extracting the roots of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 15(3)\sqrt[3]{3}+4(2)\sqrt[3]{3} \\\\= 45\sqrt[3]{3}+8\sqrt[3]{3} .\end{array} By combining like radicals, the expression above is equivalent to \begin{array}{l}\require{cancel} (45+8)\sqrt[3]{3} \\\\= 53\sqrt[3]{3} .\end{array}
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