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 - Page 466: 50



Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $ \dfrac{\sqrt{27}}{2}-\dfrac{3\sqrt{3}}{2}+\dfrac{\sqrt{3}}{\sqrt{4}} ,$ find a factor of the radicand that is a perfect power of the index. Then, extract the root of that factor. Finally, combine the like radicals. $\bf{\text{Solution Details:}}$ Rewriting the radicand with a factor that is a perfect power of the index, the given expression is equivalent to \begin{array}{l}\require{cancel} \dfrac{\sqrt{9\cdot3}}{2}-\dfrac{3\sqrt{3}}{2}+\dfrac{\sqrt{3}}{\sqrt{4}} \\\\= \dfrac{\sqrt{(3)^2\cdot3}}{2}-\dfrac{3\sqrt{3}}{2}+\dfrac{\sqrt{3}}{\sqrt{(2)^2}} .\end{array} Extracting the root of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} \dfrac{3\sqrt{3}}{2}-\dfrac{3\sqrt{3}}{2}+\dfrac{\sqrt{3}}{2} .\end{array} Combining the like radicals results to \begin{array}{l}\require{cancel} \dfrac{3\sqrt{3}-3\sqrt{3}+\sqrt{3}}{2} \\\\= \dfrac{\sqrt{3}}{2} .\end{array}
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