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: 40

Answer

$-2x\sqrt[3]{3}$

Work Step by Step

Using $a(b+c)=ab+ac$, or the Distributive Property, and the properties of radicals, the given expression, $ \sqrt[3]{x}(\sqrt[3]{3x^2}-\sqrt[3]{81x^2}) ,$ is equivalent to \begin{array}{l}\require{cancel} (\sqrt[3]{x})(\sqrt[3]{3x^2})-(\sqrt[3]{x})(\sqrt[3]{81x^2}) \\\\= \sqrt[3]{x(3x^2)}-\sqrt[3]{x(81x^2)} \\\\= \sqrt[3]{3x^3}-\sqrt[3]{81x^3} \\\\= \sqrt[3]{x^3\cdot3}-\sqrt[3]{27x^3\cdot3} \\\\= \sqrt[3]{(x)^3\cdot3}-\sqrt[3]{(3x)^3\cdot3} \\\\= x\sqrt[3]{3}-3x\sqrt[3]{3} \\\\= -2x\sqrt[3]{3} .\end{array}
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