Could i ask him out or is that doomed...?

21 year old girl, have a thing for the 26 year old clmate of my best friend. He's a quiet enough type of guy whereas i'm an alpha female...so instead of pathetically waiting around i thought maybe i'd just try and see if he was interested? I'm not amazing or anything but i'm pretty attractive, at least by the other guy's in his cl' standard. What d'you think?! and how would i ask? He broke up with his girlfriend a while ago so hence my asking now...