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 - Page 75: 73

Answer

$\color{blue}{\sqrt[3]{2}}$

Work Step by Step

RECALL: $\sqrt[m]{\sqrt[n]{a}}=\sqrt[mn]{a}$ Use the rule above to obtain: $=\sqrt[3(2)]{4} \\=\sqrt[6]{4}$ Since $4=2^2$, the expression above is equivalent to: $=\sqrt[6]{2^2}$ Use the rule $\sqrt[n]{a^m}=a^{m/n}$ to obtain: $=2^{2/6} \\=2^{1/3}$ Use the rule $a^{1/n} = \sqrt[n]{a}$ to obtain: $=\color{blue}{\sqrt[3]{2}}$
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