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: 25

Answer

$(x-2)\sqrt[3]{6x}$

Work Step by Step

Simplifying the radical terms by extracting the root of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt[3]{6x^4}-\sqrt[3]{48x} \\\\= \sqrt[3]{x^3\cdot6x}-\sqrt[3]{8\cdot6x} \\\\= \sqrt[3]{(x)^3\cdot6x}-\sqrt[3]{(2)^3\cdot6x} \\\\= x\sqrt[3]{6x}-2\sqrt[3]{6x} .\end{array} Combining the like radicals results to \begin{array}{l}\require{cancel} x\sqrt[3]{6x}-2\sqrt[3]{6x} \\\\= (x-2)\sqrt[3]{6x} .\end{array}
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