Can a cockroach survive a nuclear blast? --- Tarun, Ghazibad, India
Part of it depends on where the roach is sitting when the bomb goes off. For example, if the roach is sitting at ground zero, then no a roach cannot survive a nuclear blast. As described in this article, the effects near ground zero are catastrophic:
Destruction at these sites was total: Robertson saw a 100-foot steel tower incinerated in an instant. The largest blast he observed, code named “Smoky,” was a magnitude of 44 kilotons — about three times the force of the bomb dropped on Hiroshima. It was enough to turn sand into glass several feet deep.
If the blast can turn sand to glass and incinerate steel, then obviously no roach is going to survive if it is on the surface.
As you get further out from ground zero, the concern is radiation exposure. Roaches do much better after exposure to radiation than people do, and there are other bugs that do better than roaches. The Mythbusters confirmed this by exposing roaches and other insects to massive doses of radiation to see what would happen:
Bugs easily survive doses that would kill humans. Bugs even survive doses of radiation 100 times greater than the lethal dose for humans.
So, it is true that roaches have a better chance of surviving the radiation from a nuclear blast than humans do.
For more info see: How nuclear bombs work