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On average, cockroaches live for about one year. These insects are rather hardy, although some people think they can simply be starved to death as a means of pest control, such as if a building is left empty with no food source for a long time. In fact, the opposite is true, as the insect can go for about a month without eating anything. Likewise, roaches can survive on things that most people would not consider suitable food, even for insects. For example, they can eat such things as glue, paper, and even shoes.
Though roaches can live for about a month without food, they can only live for about one week without water. In fact, even without their heads, they can live for about a week. The only reason they die without a head is because they can't consume water with their mouths missing. Interestingly, cockroaches can even live for a time if their hearts stop.
Many people have heard that after a nuclear war, cockroaches would be the only living beings to survive. While this statement is widely made, there is no concrete scientific evidence to prove it. There is scientific evidence to suggest that roaches and similar insects are more capable of withstanding radiation than other life forms, however. Roaches can withstand up to 15 times the amount of radiation that a human being can, but when compared to other insects, they aren't abnormally radiation resistant.
The reason that cockroaches may be able to withstand radiation better than humans is the fact that their cells divide slower than those of human beings. In these bugs, cell division takes place only once during each molting time, and at most, they will molt just once weekly in their juvenile stage and not at all as adults. This means that, if radiation exposure is fleeting, roaches that were not molting during that time would not be significantly affected. Any lingering radiation would have the potential to damage their cells, however.
These insects begin their life cycles in egg capsules, which are dropped right before they hatch. A female German cockroach, for example, may carry about 40 eggs. It takes about three to four months for an egg to develop from birth to nymph to an adult.