#### Answer

$5\sqrt{2}+2$

#### Work Step by Step

Using $a(b+c)=ab+ac$ or the Distributive Property, the given expression, $
\sqrt{2}(5+\sqrt{2})
,$ is equivalent to
\begin{array}{l}\require{cancel}
5\sqrt{2}+\sqrt{2(2)}
\\\\=
5\sqrt{2}+\sqrt{4}
.\end{array}
Using the properties of radicals, the expression above simplifies to
\begin{array}{l}\require{cancel}
5\sqrt{2}+\sqrt{(2)^2}
\\\\=
5\sqrt{2}+2
.\end{array}