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: 44

Answer

$\sqrt{35}+\sqrt{14}-\sqrt{10}-2$

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{7}-\sqrt{2})\sqrt{5}+\sqrt{2}) ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt{7}(\sqrt{5})+\sqrt{7}(\sqrt{2})-\sqrt{2}(\sqrt{5})-\sqrt{2}(\sqrt{2}) \\\\= \sqrt{7(5)}+\sqrt{7(2)}-\sqrt{2(5)}-\sqrt{(2)^2} \\\\= \sqrt{35}+\sqrt{14}-\sqrt{10}-2 .\end{array}
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