Answer
$d=\sqrt{95}$
Work Step by Step
Using $d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$ (or the Distance Formula), then the distance, $d$, between the given points $
(-2\sqrt{5},\sqrt{10}) \text{ and } (-\sqrt{5},4\sqrt{10})
,$ is
\begin{array}{l}\require{cancel}
d=\sqrt{(-2\sqrt{5}-(-\sqrt{5}))^2+(\sqrt{10}-4\sqrt{10})^2}
\\\\
d=\sqrt{(-2\sqrt{5}+\sqrt{5})^2+(\sqrt{10}-4\sqrt{10})^2}
\\\\
d=\sqrt{(-\sqrt{5})^2+(-3\sqrt{10})^2}
\\\\
d=\sqrt{5+9\cdot10}
\\\\
d=\sqrt{5+90}
\\\\
d=\sqrt{95}
.\end{array}
