Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 8 - Section 8.2 - Multiplying and Dividing Radicals - Exercise Set: 103

Answer

$2\sqrt[4]{2}$

Work Step by Step

Using $\sqrt{x}\cdot\sqrt{y}=\sqrt{xy}$ or the product rule of radicals, the given expression, $ \sqrt[4]{4}\cdot\sqrt[4]{8} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt[4]{4(8)} \\\\= \sqrt[4]{32} \\\\= \sqrt[4]{16\cdot2} \\\\= \sqrt[4]{(2)^2\cdot2} \\\\= 2\sqrt[4]{2} .\end{array}
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