Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Sections 7.1-7.5 - Integrated Review - Radicals and Rational Exponents - Page 447: 31

Answer

$\sqrt[]{15} - \sqrt[]{6}$

Work Step by Step

Using the Distributive Property and the properties of radicals, the given expression, $ \sqrt[]{3}\left( \sqrt{5}-\sqrt{2} \right) ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt[]{3}\left( \sqrt{5} \right) - \sqrt[]{3}\left(\sqrt{2} \right) \\\\= \sqrt[]{3(5)} - \sqrt[]{3(2)} \\\\= \sqrt[]{15} - \sqrt[]{6} .\end{array}
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