College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.7 - Radical Expressions - R.7 Exercises - Page 68: 72



Work Step by Step

$\bf{\text{Solution Outline:}}$ To add/subtract the given expression, $ \sqrt[3]{32}-5\sqrt[3]{4}+2\sqrt[3]{108} ,$ simplify first each radical term by extracting the factor that is a perfect power of the index. Then, combine the like radicals. $\bf{\text{Solution Details:}}$ Extracting the factors of each radicand that is a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt[3]{8\cdot4}-5\sqrt[3]{4}+2\sqrt[3]{27\cdot4} \\\\= \sqrt[3]{(2)^3\cdot4}-5\sqrt[3]{4}+2\sqrt[3]{(3)^3\cdot4} \\\\= 2\sqrt[3]{4}-5\sqrt[3]{4}+2(3)\sqrt[3]{4} \\\\= 2\sqrt[3]{4}-5\sqrt[3]{4}+6\sqrt[3]{4} .\end{array} By combining the like radicals, the expression above simplifies to \begin{array}{l}\require{cancel} (2-5+6)\sqrt[3]{4} \\\\= 3\sqrt[3]{4} .\end{array}
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