Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 7 - Section 7.3 - Simplifying Radicals, the Distance Formula, and Circles - 7.3 Exercises: 100

Answer

$\dfrac{y^{5}\sqrt[3]{y^2}}{5}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $ \sqrt[3]{\dfrac{y^{17}}{125}} ,$ find a factor of the radicand that is a perfect power of the index. Then extract the root of that factor. Note that all variables are assumed to represent positive real numbers. $\bf{\text{Solution Details:}}$ Expressing the radicand of the expression above with a factor that is a perfect power of the index and then extracting the root of that factor results to \begin{array}{l}\require{cancel} \sqrt[3]{\dfrac{y^{15}}{125}\cdot y^2} \\\\= \sqrt[3]{\left( \dfrac{y^{5}}{5} \right)^3\cdot y^2} \\\\= \dfrac{y^{5}}{5}\sqrt[3]{y^2} \\\\= \dfrac{y^{5}\sqrt[3]{y^2}}{5} .\end{array}
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