Answer
$4+3\sqrt{6}$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$, or the product of 2 binomials, and the properties of radicals, the given expression, $
(2+\sqrt{6})(5-\sqrt{6})
,$ is equivalent to
\begin{array}{l}\require{cancel}
2(5)+2(-\sqrt{6})+\sqrt{6}(5)+\sqrt{6}(-\sqrt{6})
\\\\=
10-2\sqrt{6}+5\sqrt{6}-\sqrt{6(6)}
\\\\=
10+3\sqrt{6}-\sqrt{(6)^2}
\\\\=
10+3\sqrt{6}-6
\\\\=
4+3\sqrt{6}
.\end{array}
