#### Answer

$-2$

#### Work Step by Step

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}