The radiation from a nuclear bomb that has been set off can spread as far as 4.69 to 5 miles from the place where the nuclear bomb blast occurred.
Usually though at that distance you're pretty safe from radiation poisoning or death from the radiation but you should still take precautions and shelter when advised to do so and when possible.
If you're out in the open with no shield from the nuclear bomb or radiation then being as close as 1.86 to 2 miles away from the nuclear bomb blast can cause radiation poisoning or death.
If there's warning of a nuclear bomb blast take shelter immediately or leave the area until safe to return.