College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.7 - Radical Expressions - R.7 Exercises - Page 68: 69



Work Step by Step

$\bf{\text{Solution Outline:}}$ To add/subtract the given expression, $ 8\sqrt{2x}-\sqrt{8x}+\sqrt{72x} ,$ simplify first each radical term by extracting the factor that is a perfect power of the index. Then, combine the like radicals. $\bf{\text{Solution Details:}}$ Extracting the factors of each radicand that is a perfect power of the index results to \begin{array}{l}\require{cancel} 8\sqrt{2x}-\sqrt{4\cdot2x}+\sqrt{36\cdot2x} \\\\= 8\sqrt{2x}-\sqrt{(2)^2\cdot2x}+\sqrt{(6)^2\cdot2x} \\\\= 8\sqrt{2x}-2\sqrt{2x}+6\sqrt{2x} .\end{array} By combining the like radicals, the expression above simplifies to \begin{array}{l}\require{cancel} (8-2+6)\sqrt{2x} \\\\= 12\sqrt{2x} .\end{array}
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