Answer
-17
Work Step by Step
$\sqrt -17\times\sqrt -17=\sqrt (-1\times17)\times\sqrt (-1\times17)=\sqrt -1\times\sqrt 17\times\sqrt -1\times\sqrt 17=i\times i\times\sqrt 17\times\sqrt 17=i^{2}\times(\sqrt 17)^{2}=-1\times17=-17$
We know that $\sqrt -1=i$, because $i^{2}=-1$.