Is it possible for one nuke to take out the world?

Maybe. The effects of a nuclear weapon are wide spread. When the bomb was dropped in Japan ( and it was nothing like what we have today) it imploded and then exploded. What this means is that it collapsed on itself and took all the air then it exploded. People miles away from the center of the explosion were burned instantly, water evaporated instantly, and anything standing was gone. The second factor is radiation levels and the sickness that follows. It also stays in the environment for thousands of years and plants, soil, animals are effected. If enough nuclear weapons are employed there will also be a nuclear winter because the suns rays will be blocked by debris in the atmosphere. So, people who survived the blast will have to contend with no services, no hospitals, radiation sickness, cold weather, and lack of food. If a bomb was employed in a place like North Korea not only would North Korea be effected but the entire area would be gone. We have thousands of American forces sitting in South Korea that would die along with the North. The use of nuclear weapons is not an answer to problems.