Answer
$23+7\sqrt{7}$
Work Step by Step
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the given expression, $
(2+\sqrt{7})(1+3\sqrt{7})
,$ is equivalent to
\begin{align*}
&
2(1)+2(3\sqrt{7})+\sqrt{7})(1)+\sqrt{7}(3\sqrt{7})
\\&=
2+6\sqrt{7}+\sqrt{7}+3(7)
\\&=
2+6\sqrt{7}+\sqrt{7}+21
\\&=
(2+21)+(6\sqrt{7}+\sqrt{7})
&\left( \text{combine like terms} \right)
\\&=
23+7\sqrt{7}
.\end{align*}
Hence, the product of the given expression is $
23+7\sqrt{7}
$.
