Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.3 - Multiplying and Simplifying Radical Expressions - Exercise Set: 72

Answer

$2\sqrt[4]{2}$

Work Step by Step

RECALL: For any non-negative real numbers a and b, $\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{ab}$ Use the rule above to obtain: $=\sqrt[4]{(4)(8)} \\=\sqrt[4]{32}$ Factor the radicand (expression inside the radical sign) so that at least one factor is a perfect fourth root, and then simplify to obtain: $\\=\sqrt[4]{16(2)} \\=\sqrt[4]{2^4(2)} \\=2\sqrt[4]{2}$
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