If a cockroach loses its head, it can live for about 2 weeks since it has other “brains” on its legs.
It finally dies because it has no mouth to get food and water.
Generally, cockroaches can live for four weeks without food, but cannot survive for more than two weeks without water.
You‘ve probably heard the story about cockroaches surviving a nuclear war: we die but they live! Radiologists have found that humans can safely withstand a one-time exposure of 5 rems (A “rem” is the dosage of radiation that will cause a specific, measured amount of injury to human tissue). A lethal dose is 800 rems or more (people are exposed to about 16 rems during their lifetime). Insect researchers have found that cockroaches can tolerate a much higher dose. The lethal dose for the American cockroach is 67,500 rems and for the German cockroach it is between 90,000 and 105,000 rems! In truth the amount of radiation that cockroaches can withstand is equivalent to that of a thermonuclear explosion.