Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 6 - Radical Functions and Rational Exponents - 6-2 Multiplying and Dividing Radical Expressions - Practice and Problem-Solving Exercises - Page 372: 77

Answer

$2\sqrt{5}$

Work Step by Step

Extracting the factors that are perfect powers of the index, the given expression, $ \sqrt{\sqrt[3]{8000}} ,$ is equivalent to \begin{align*}\require{cancel} & \sqrt{\sqrt[3]{(20)^3}} \\\\&= \sqrt{20} \\\\&= \sqrt{4\cdot5} \\\\&= \sqrt{2^2\cdot5} \\\\&= 2\sqrt{5} .\end{align*} Hence, the given expression simplifies to $ 2\sqrt{5} $.
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