Well first, not all radiation is equal. A radiation suit can prevent penetration by alpha particles (helium nuclei) or beta particles (electrons), but not neutrons or gamma rays. In addition to blocking heavier particles, suits also keep the person wearing them from getting dust containing radioactive isotopes on them or in their lungs. Washing the exterior of the suits with soapy water just removes this dust so it doesn’t spread and irradiate other people/places.
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