If the head of cockroach is cut off, it will still live for as long as

The nervous system of a cockroach is distributed throughout its body. While the head does contain a portion of the nervous system, the majority of it is located along the ventral (belly-side) part of the body. This distribution allows a cockroach to continue functioning even if its head is severed. In such cases, the cockroach can survive for a period of time, usually up to a week, because its basic bodily functions and reflexes are controlled by the nerve ganglia located in the abdomen rather than the head.