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 - Page 660: 26



Work Step by Step

Simplifying each term and then combining like terms, the given expression, $ \sqrt[3]{54x}-\sqrt[3]{2x^4} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt[3]{27\cdot2x}-\sqrt[3]{x^3\cdot2x} \\\\= \sqrt[3]{(3)^3\cdot2x}-\sqrt[3]{(x)^3\cdot2x} \\\\= 3\sqrt[3]{2x}-x\sqrt[3]{2x} \\\\= (3-x)\sqrt[3]{2x} .\end{array} * Note that it is assumed that all variables represent positive numbers.
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