Quote (from the RHS website):
"To prevent shrivelling in vegetables which lose moisture such as carrots, celeriac, swedes and beetroot, store the roots in layers of moist sand or peat-substitute in boxes, in a frost-free, dark place such as a shed or cellar"
https://www.rhs.org.uk/vegetables/root-vegetables-storing
If you're buying from supermarkets though, the obvious solution would simply to be to buy only what you'll need to use within the next few days, rather than buying loads at once.