It is popularly suggested that cockroaches will “inherit the earth” if humanity destroys itself in a nuclear war. While cockroaches do, indeed, have a much higher radiation resistance than vertebrates, with a lethal dose perhaps six to 15 times that for humans, they are not exceptionally radiation-resistant compared to other insects, such as the fruit fly.- Nuclear warfare (Wikipedia)
Nuclear warfare, also known as atomic warfare, is a military conflict or prepared political strategy that deploys nuclear weaponry. Nuclear weapons are weapons of mass destruction; in contrast to conventional warfare, nuclear warfare can produce destruction in a much shorter time and can have a long-lasting radiological result. A major nuclear exchange would likely have long-term effects, primarily from the fallout released, and could also lead to secondary effects, such as “nuclear winter”, nuclear famine, and societal collapse. A global thermonuclear war with Cold War-era stockpiles, or even with the current smaller stockpiles, may lead to various scenarios including the extinction of the human species.