Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set: 21

Answer

$9\sqrt[3]{2}$

Work Step by Step

Simplifying each term and then combining like terms, the given expression, $ 3\sqrt[3]{16}+\sqrt[3]{54} ,$ is equivalent to \begin{array}{l}\require{cancel} 3\sqrt[3]{8\cdot2}+\sqrt[3]{27\cdot2} \\\\= 3\sqrt[3]{(2)^3\cdot2}+\sqrt[3]{(3)^3\cdot2} \\\\= 3\cdot2\sqrt[3]{2}+3\sqrt[3]{2} \\\\= 6\sqrt[3]{2}+3\sqrt[3]{2} \\\\= 9\sqrt[3]{2} .\end{array}
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