Answer
$d=\sqrt{93}\approx9.64$
Work Step by Step
$(3\sqrt{3}, \sqrt{5})$ and $(-\sqrt{3}, 4\sqrt{5})$
The distance between two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is $d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$
Substitute the given points into the formula and evaluate:
$d=\sqrt{(-\sqrt{3}-3\sqrt{3})^{2}+(4\sqrt{5}-\sqrt{5})^{2}}=...$
$...=\sqrt{(-4\sqrt{3})^{2}+(3\sqrt{5})^{2}}=\sqrt{(16)(3)+(9)(5)}=...$
$...=\sqrt{48+45}=\sqrt{93}\approx9.64$