Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - R.7 Radical Expressions - R.7 Exercises: 74

Answer

$\color{blue}{\sqrt[4]{5}}$

Work Step by Step

RECALL: $\sqrt[m]{\sqrt[n]{a}}=\sqrt[mn]{a}$ Use the rule above to obtain: $=\sqrt[4(2)]{25} \\=\sqrt[8]{25}$ Since $25=5^2$, the expression above is equivalent to: $=\sqrt[8]{5^2}$ Use the rule $\sqrt[n]{a^m}=a^{m/n}$ to obtain: $=5^{2/8} \\=5^{1/4}$ Use the rule $a^{1/n} = \sqrt[n]{a}$ to obtain: $=\color{blue}{\sqrt[4]{5}}$
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