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: 14

Answer

$13\sqrt{2}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $ 5\sqrt{8}+3\sqrt{72}-3\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} 5\sqrt{4\cdot2}+3\sqrt{36\cdot2}-3\sqrt{25\cdot2} \\\\= 5\sqrt{(2)^2\cdot2}+3\sqrt{(6)^2\cdot2}-3\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} 5(2)\sqrt{2}+3(6)\sqrt{2}-3(5)\sqrt{2} \\\\= 10\sqrt{2}+18\sqrt{2}-15\sqrt{2} .\end{array} By combining like radicals, the expression above is equivalent to \begin{array}{l}\require{cancel} (10+18-15)\sqrt{2} \\\\= 13\sqrt{2} .\end{array}
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