Answer
$\dfrac{52\sqrt{5}}{5}$
Work Step by Step
Using the properties of radicals, the given expression, $
4\sqrt{20}-\dfrac{3}{\sqrt{5}}+\sqrt{45}
,$ simplifies to
\begin{array}{l}\require{cancel}
4\sqrt{4\cdot5}-\dfrac{3}{\sqrt{5}}\cdot\dfrac{\sqrt{5}}{\sqrt{5}}+\sqrt{9\cdot5}
\\\\=
4\sqrt{(2)^2\cdot5}-\dfrac{3\sqrt{5}}{5}+\sqrt{(3)^2\cdot5}
\\\\=
4(2)\sqrt{5}-\dfrac{3\sqrt{5}}{5}+3\sqrt{5}
\\\\=
8\sqrt{5}-\dfrac{3\sqrt{5}}{5}+3\sqrt{5}
\\\\=
\dfrac{40\sqrt{5}}{5}-\dfrac{3\sqrt{5}}{5}+\dfrac{15\sqrt{5}}{5}
\\\\=
\dfrac{52\sqrt{5}}{5}
.\end{array}
