Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - Test: Chapter 10: 16

Answer

$9\sqrt{2xy}$

Work Step by Step

Extracting the factors that are perfect powers of the index, the given expression simplifies to \begin{array}{l}\require{cancel} \sqrt{50xy}+\sqrt{72xy}-\sqrt{8xy} \\\\= \sqrt{25\cdot2xy}+\sqrt{36\cdot 2xy}-\sqrt{4\cdot 2xy} \\\\= \sqrt{(5)^2\cdot2xy}+\sqrt{(6)^2\cdot 2xy}-\sqrt{(2)^2\cdot 2xy} \\\\= 5\sqrt{2xy}+6\sqrt{2xy}-2\sqrt{2xy} .\end{array} By combining like radicals, the given expression simplifies to \begin{array}{l}\require{cancel} 5\sqrt{2xy}+6\sqrt{2xy}-2\sqrt{2xy} \\\\= (5+6-2)\sqrt{2xy} \\\\= 9\sqrt{2xy} .\end{array}
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