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: 35

Answer

$6\sqrt{5}-4$

Work Step by Step

Using $a(b+c)=ab+ac$ or the Distributive Property and the properties of radicals, the given expression, $ \sqrt{2}(3\sqrt{10}-\sqrt{8}) ,$ is equivalent to \begin{array}{l}\require{cancel} (\sqrt{2})(3\sqrt{10})-(\sqrt{2})(\sqrt{8}) \\\\= 3\sqrt{2(10)}-\sqrt{2(8)} \\\\= 3\sqrt{20}-\sqrt{16} \\\\= 3\sqrt{4\cdot5}-\sqrt{16} \\\\= 3\sqrt{(2)^2\cdot5}-\sqrt{(4)^2} \\\\= 3\cdot2\sqrt{5}-4 \\\\= 6\sqrt{5}-4 .\end{array}
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