Put root vegetables like carrots, parsnips, radishes, turnips, and beets in the refrigerator. Carrots and parsnips will stay fresh in the fridge for up to 3 weeks. Radishes, turnips, and beets will last about 2 weeks. Instead of the fridge, it's best to keep potatoes and sweet potatoes in the pantry or a cool, dark place. Potatoes that you store in the fridge may darken when you cook them and taste sweet.