>>12561796"radiation" doesn't mean a thing. nuclear fallout is mainly big radioactive particles mixing with the environement (dirt, dust, water etc...)
to answer your question, nothing incredible would happen to water if you exposed it to alpha, beta and gamma radiation. you would get some atom splitting, so a shitty way to do get oxygen and hydrogen from water.
the same happens when "mixing" radioactive materials with water : you get radioactive materials in water. You get sick when drinking it because the radioactive materials in the water (not the water iteself) fuck with your internal organs, or your skin if you swim in it though you would need a shit ton of radioactive stuff, as water itself is a very good insulator for radiation.
Nothing happens to the water itself and once filtered you'd get pure wah ah..