Chapter 9 - Roots and Radicals - 9.4 - Products and Quotients Involving Radicals - Problem Set 9.4 - Page 418: 38

$7$

Using $(a+b)(a-b)=a^{2}+b^{2}$, or the Distributive Property, and the properties of radicals, the given expression, $ (\sqrt{11}-2)(\sqrt{11}+2) ,$ simplifies to \begin{array}{l}\require{cancel} (\sqrt{11})^2-(2)^2 \\\\= 11-4 \\\\= 7 .\end{array}