Answer
$8+4\sqrt{5}$
Work Step by Step
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the given expression, $
(3+\sqrt{5})(1+\sqrt{5})
,$ is equivalent to
\begin{align*}
&
3(1)+3(\sqrt{5})+\sqrt{5}(1)+\sqrt{5}(\sqrt{5})
\\&=
3+3\sqrt{5}+\sqrt{5}+5
\\&=
(3+5)+(3\sqrt{5}+\sqrt{5})
&\left( \text{combine like terms} \right)
\\&=
8+4\sqrt{5}
.\end{align*}
Hence, the product of the given expression is $
8+4\sqrt{5}
$.
