Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - 9.2 - Simplifying Radicals - Problem Set 9.2: 57

Answer

$18\sqrt[3]{2}$

Work Step by Step

Using the properties of radicals, the given expression, $ 2\sqrt[3]{54}+6\sqrt[3]{16} ,$ simplifies to \begin{array}{l}\require{cancel} 2\sqrt[3]{27\cdot2}+6\sqrt[3]{8\cdot2} \\\\= 2\sqrt[3]{(3)^3\cdot2}+6\sqrt[3]{(2)^3\cdot2} \\\\= 2\cdot3\sqrt[3]{2}+6\cdot2\sqrt[3]{2} \\\\= 6\sqrt[3]{2}+12\sqrt[3]{2} \\\\= 18\sqrt[3]{2} .\end{array}
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