Let's say survivors in the area contaminated by radioactive fallout need to somehow process the water from rivers, rain or pipes. How could they go about it? Is it even possible to 'remove radioactivity' from the water?
The water itself isn't radioactive, rather particles dissolved in it, because water is a quite good solvent. Therefore, filtration (e.g. with activated carbon) or precipitation can remove such particles. Also a ion exchanger can remove radioactive species. But this can take quite long, especially if the needed amount is large.