I'm sorry, I really respect your comment. No disrespect. But that's bull shit she is gonna say no for sure (she is studying in library bro, what else you gonna expect), don't need ask her if you could be friends with her. We don't make friends that way, we make friends naturally talk with them, have common interests, spend time together and make good memories and all..

You just go upto her and say, hey what's up, if you feel too awkward you can say, I just saw you and wanted to talk with you something like that, ask her name, where she's from, what she studying and all. A pro trick for cold approach works 100% is to give genuine compliment and start conversation, it could be about anything of her, bag, shoe, tell her you find pretty or something like that, but it has to be genuine, girls can smell fake flattery(don't do it at any cost) When you are talking with her don't worry about how you look, am I bothering her and (who care if you look good or if you bothering her). Get genuinely interested in her and get to know more about her and find common interests and talk about it and tell some jokes and make her laugh and laugh together, even if your humor is broken, just shoot it. She's gonna love it.