Chapter 10 - Exponents and Radicals - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set - Page 661: 46

$-2$

Using $(a+b)(a-b)=a^2-b^2$, or the product of the sum and difference of like terms, and the properties of radicals, the given expression, $ (3+\sqrt{11})(3-\sqrt{11}) ,$ is equivalent to \begin{array}{l}\require{cancel} 3^2-(\sqrt{11})^2 \\\\= 9-11 \\\\= -2 .\end{array}