Possible answers:
Yes: cockroaches never die, they are immortal.
No: cockroaches die; they can be killed.
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Cockroaches are easy to kill, just step on them.
Cockroaches aren't immortal. They will eventually die, although they can live several weeks without their head. But if you squish them, preferably on their tummy's they can die. But it can be quite difficult to kill them on their backs, as they have hard shells.
They are susceptible to a good dose of chemical warfare. You can buy a little death chamber for them, which you bait and put on the floor. Also, make sure to clean your house carefully to try and starve them.
Smash them with your shoe. They will DEFINITELY die, but they can live a couple weeks without their head, eventually they die though.
No, they don't actually. For example, they can die by just spraying insect spray on them or by stepping on them, although they can even survive nuclear bombs.
Yes. They live for a max of a year or they get poisoned/crushed.
I'm sure the one I stepped on a few days ago is pretty dead.
Why kill them? They are alive persons and have their own souls. They have kids and parents. And they have rights you know. Your question makes cockroaches sad :(