Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4 - Page 418: 37

$15$

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}