Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4: 37

Answer

$15$

Work Step by Step

Using $(a+b)(a-b)=a^{2}-b^{2}$, or the Distributive Property, and the properties of radicals, the given expression, $ (5+\sqrt{10})(5-\sqrt{10}) ,$ simplifies to \begin{array}{l}\require{cancel} (5)^2-(\sqrt{10})^2 \\\\= 25-10 \\\\= 15 .\end{array}
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