Answer
$-7\sqrt{5}$
Work Step by Step
Simplifying each term and then combining like terms, the given expression, $
3\sqrt{45}-8\sqrt{20}
,$ is equivalent to
\begin{array}{l}\require{cancel}
3\sqrt{9\cdot5}-8\sqrt{4\cdot5}
\\\\=
3\sqrt{(3)^2\cdot5}-8\sqrt{(2)^2\cdot5}
\\\\=
3\cdot3\sqrt{5}-8\cdot2\sqrt{5}
\\\\=
9\sqrt{5}-16\sqrt{5}
\\\\=
-7\sqrt{5}
.\end{array}
