Well, hostas are perennials and that 'new' plant you bought is most likely a division from a bigger plant, Greg. So that bigger root came from the mama plant probably.
Something definitely had a bite out of it where the white stuff is showing. No way really to tell, unless you can see tooth marks with a magnifying glass? Bunny or squirrel, mouse or deer? (no deer would eat the leaves) Unless you actually see the critter, it doesn't really matter.
But I'd get those roots covered up with soil again, put some mulch over top and sprinkle something like cayenne pepper around the plant to discourage whoever it was from returning for another snack. Also if you haven't already, put out a little bit of slug bait around those new hostas. Slugs and snails just love them.
