[18/m] Should I approach [18/f] crush even though I think she is way out of my league?

Theres a girl I see around campus and around the school caf. I think shes freakin gorgeous. I've been looking for a way to talk to her and I've made up my mind to approach her. This will be the first girl that I'm actually approaching. I thought the saying of being stunned by beauty was cliche until I saw her. I'm a pretty shy and quiet person but I feel like I have to at least try or introduce myself. I think that she is way out of my league. I know a friend of hers and he told me she basically has a preference to Black guys. I'm Black but I don't know if I fit the mold of what she might be looking for. How do I approach her. And should I ask her for her number if I can manage to not choke when trying to talk to her?

Any tips are appreciated