Answer
$7\sqrt {2}$ units $\approx9.899$ units
Work Step by Step
Let $P=(x_{1},y_{1})=(-\sqrt 2,0)$ and $Q=(x_{2},y_{2})=(0,-4\sqrt 6)$
Finding the distance between P and Q,
$d(P,Q)=\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2})}$
$d(P,Q)=\sqrt {(0-(-\sqrt 2))^{2}+(-4\sqrt 6-0)^{2}}$
$d(P,Q)=\sqrt {(\sqrt 2)^{2}+(-4\sqrt 6)^{2}}$
$d(P,Q)=\sqrt {2+16(6)}$
$d(P,Q)=\sqrt {2+96}$
$d(P,Q)=\sqrt {98}$
$d(P,Q)=\sqrt {49\times2}$
$d(P,Q)=7\sqrt {2}\approx9.899$
