The best way to kill a cockroach:
1) Get him running across an open space while you are holding a large, heavy book (I have found literature collections to be great for this)
2) Hold the book right above his running path and then DROP it . This will smash him well.
3) After a few days - when you are out of large, heavy literature books to drop - pick up the books (which may or may not have been sitting there for a while) and scrape the corpses from the bottom into the toilet.
Cockroaches, ants... you stop sweating this kind of thing when you live in a place like this; you just learn to kill kill kill. And you get really good at it and share your killing strategies with others. You stop sweating it until you realize you are killing way too many of them on a regular basis and you think that they are coming from inside the box that is lodged in the corner of your Rapunzel Room bathroom ceiling.
Then you tell your landlord, who is usually pretty responsive. He may tell you to go and buy a can of Raid, but don't let him pull that one on you like I did. I let him pull that one on me for a week, until I could see multiple antennae coming out of the box and hear them like a carnival at night and until Katherine found one on her bed and until I came home to five of them on my bathroom floor. Then I sent him a text late at night that said, "We can't live like this anymore. Please get a professional exterminator here tomorrow."
He did get one, and we came home to many, many cockroach corpses. I guess we will be coming home to them for a while now. Big ones, little itty baby ones... the cockroaches are dying. When I asked how many were in the nest in the box in my bathroom, he smiled, shook his head and said, "Many."
That is the best way to kill a cockroach.