Plan a fighter jet to be at her house the same time you go over to "study". Get the FBI to play along. Once you're in the house have the jet swoop in and act like they're taking the both of you hostage. She'll be very scared. Ask her to hang on to you. Once you're on the plane make a fight scene with the FBI and make it look real. "Save her life" so to say. Then land the plane at a nearby mall. Say "how convenient. I was just going to rent a tux for prom. Won't you join me?" If she says no then say "you realize I just saved your life?" If she says no again cut out her voice box so she can't say no. It's a sure way to get a date my fine friend.
In a big way! All girls want a guy to ask them in a cute big way trust me haha. If you're really good friends with her make it meaningful with things you guys did together or what she likes :) good luck!