Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.4 - Adding and Subtracting Radical Expressions - 7.4 Exercises: 32

Answer

$16\sqrt[4]{2}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $ 2\sqrt[4]{512}+4\sqrt[4]{32} ,$ simplify first each term by expressing the radicand as a factor that is a perfect power of the index. Then, extract the root. Finally, combine the like radicals. $\bf{\text{Solution Details:}}$ Expressing the radicand as an expression that contains a factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 2\sqrt[4]{256\cdot2}+4\sqrt[4]{16\cdot2} \\\\= 2\sqrt[4]{(4)^2\cdot2}+4\sqrt[4]{(2)^2\cdot2} .\end{array} Extracting the roots of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 2(4)\sqrt[4]{2}+4(2)\sqrt[4]{2} \\\\= 8\sqrt[4]{2}+8\sqrt[4]{2} .\end{array} By combining like radicals, the expression above is equivalent to \begin{array}{l}\require{cancel} (8+8)\sqrt[4]{2} \\\\= 16\sqrt[4]{2} .\end{array}
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