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 - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set: 43

Answer

$\sqrt{6}-\sqrt{14}+\sqrt{21}-7$

Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$, or the product of 2 binomials, and the properties of radicals, the given expression, $ (\sqrt{2}+\sqrt{7})\sqrt{3}-\sqrt{7}) ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt{2}(\sqrt{3})+\sqrt{2}(-\sqrt{7})+\sqrt{7}(\sqrt{3})+\sqrt{7}(-\sqrt{7}) \\\\= \sqrt{2(3)}-\sqrt{2(7)}+\sqrt{7(3)}-\sqrt{7(7)} \\\\= \sqrt{6}-\sqrt{14}+\sqrt{21}-\sqrt{(7)^2} \\\\= \sqrt{6}-\sqrt{14}+\sqrt{21}-7 .\end{array}
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