Intermediate Algebra (12th Edition)

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

Chapter 7 - Section 7.4 - Adding and Subtracting Radical Expressions - 7.4 Exercises: 39

Answer

$4t\sqrt[3]{3st}-3s\sqrt{3st}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $ \sqrt[3]{192st^4}-\sqrt{27s^3t} ,$ simplify first each term by expressing the radicand as a factor that is a perfect power of the index. Then, extract the root. $\bf{\text{Solution Details:}}$ Expressing the radicand as an expression that contains a factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt[3]{64t^3\cdot3st}-\sqrt{9s^2\cdot 3st} \\\\= \sqrt[3]{(4t)^3\cdot3st}-\sqrt{(3s)^2\cdot 3st} .\end{array} Extracting the roots of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 4t\sqrt[3]{3st}-3s\sqrt{3st} .\end{array}
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