They should last about a week in the fridge. If they start to look or smell bad, then you should discard them. Ise a perforated bag to make them last more. When storing them whole, place them loosely in a bowl, cover them with food-safe plastic wrap, and then make some holes. If cutting them before storing, make sure to trim the ends where the dirt holds and then place the cut or shredded sprouts in a food-safe plastic container for up to 3 days.