Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - Mid-Chapter Review - Mixed Review: 24

Answer

$15\sqrt[3]{5}$

Work Step by Step

Extracting the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt[3]{5000}+\sqrt[3]{625} \\\\= \sqrt[3]{1000\cdot5}+\sqrt[3]{125\cdot5} \\\\= \sqrt[3]{(10)^3\cdot5}+\sqrt[3]{(5)^3\cdot5} \\\\= 10\sqrt[3]{5}+5\sqrt[3]{5} \\\\= 15\sqrt[3]{5} .\end{array}
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