Answer
$$-13$$
Work Step by Step
Recall that the definition $\sqrt{-a}=i\sqrt{a}$ must be applied BEFORE the other rules regarding radicals, therefore,
$\sqrt{-13}* \sqrt{-13} = i\sqrt{13} * i\sqrt{13}$
now you may multiply:
$i^2(13)$
$(-1)(13)$
$$-13$$
which checks out because $(\sqrt{a})^2 = a$