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: 40

Answer

$5a^2b^2\sqrt{5ab}+5ab\sqrt[3]{ab}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $ \sqrt{125a^5b^5}+\sqrt[3]{125a^4b^4} ,$ 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{25a^4b^4\cdot5ab}+\sqrt[3]{125a^3b^3\cdot ab} \\\\= \sqrt{(5a^2b^2)^2\cdot5ab}+\sqrt[3]{(5ab)^3\cdot ab} .\end{array} Extracting the roots of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 5a^2b^2\sqrt{5ab}+5ab\sqrt[3]{ab} .\end{array}
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