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I gather that it'd keep in a root cellar, though I have never had a successful root cellar experience even for uncut vegetables.  For a span of a couple of days, it has always sounded like (goofy as it sounds) people also sometimes submerge the sweet potato in a bowl of water in the refrigerator, but I haven't ever actually tried that, either.

For my own solution, I dice (or shred) and freeze them.  Freezing the whole thing would probably work, too, but then you'd need to worry about texture when it thaws.