Yes if they are sheltered from the initial extreme temperatures which would toast them. The remaining effects due to radiation are within the roach (species) toleration although individual roaches may die. That's how evolution works.
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There is a possibility for a cockroach to live and die. A cockroach will die from the initial blast, meaning the cockroach will die from the fiery explosion. A cockroach will survive the radiation of the blast, but not the actual blast itself.
A fire bomb is a conventional incendiary bomb: magnesium, napalm, etc. A nuclear bomb uses fission and/or fusion and is mostly a blast effect weapon.
The cold war is over but Russia may attack us with nuclear weapons. Get in a bomb shelter and pray like hell you won't turn into some fugluy creature.
Most insects have a far higher LD50 for ionizing radiation than any mammal, but its a myth that cockroaches will survive nuclear war.
Sure. A nuke has 3 main lethal features: 1- Blast (high pressure wave). Roaches are more resistant to blasts than a person, but only to a point. 2- Heat. It might be easier for a roach to find shelter from the intense heat than it would be for a person, but if we're talking tens of thousands of degrees Celsius, lil' roachy is toast. 3- Radiation. Although roaches can tolerate exposure to radiation better than people can, they are not radiation proof. Given a high enough dose, cockroaches will die.