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: 13

Answer

$24\sqrt{2}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $ 6\sqrt{18}-\sqrt{32}+2\sqrt{50} ,$ simplify first each term by expressing the radicand as a factor that is a perfect power of the index. Then, extract the root. Finally, combine the like radicals. $\bf{\text{Solution Details:}}$ 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} 6\sqrt{9\cdot2}-\sqrt{16\cdot2}+2\sqrt{25\cdot2} \\\\ 6\sqrt{(3)^2\cdot2}-\sqrt{(4)^2\cdot2}+2\sqrt{(5)^2\cdot2} .\end{array} Extracting the roots of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 6(3)\sqrt{2}-4\sqrt{2}+2(5)\sqrt{2} \\\\= 18\sqrt{2}-4\sqrt{2}+10\sqrt{2} .\end{array} By combining like radicals, the expression above is equivalent to \begin{array}{l}\require{cancel} (18-4+10)\sqrt{2} \\\\= 24\sqrt{2} .\end{array}
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