Answer
$\sqrt{93}$
Work Step by Step
The distance formula from $P_1(x_1,y_1)$ to $P_2(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
Hence here: $d=\sqrt{(3\sqrt3-(-\sqrt3))^2+(\sqrt5-4\sqrt5))^2}=\sqrt{(4\sqrt3)^2+(-3\sqrt5)^2}=\sqrt{48+45}=\sqrt{93}$