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: 12

Answer

$\sqrt[4]{5}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $ \sqrt[4]{405}-2\sqrt[4]{5} ,$ 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} \sqrt[4]{81\cdot5}-2\sqrt[4]{5} \\\\ \sqrt[4]{(3)^4\cdot5}-2\sqrt[4]{5} .\end{array} Extracting the roots of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 3\sqrt[4]{5}-2\sqrt[4]{5} .\end{array} By combining like radicals, the expression above is equivalent to \begin{array}{l}\require{cancel} (3-2)\sqrt[4]{5} \\\\= 1\sqrt[4]{5} \\\\= \sqrt[4]{5} .\end{array}
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