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I never peel mine and have suffered no ill effects. You might wanna scrub it, though. Or eat baby carrots.
sometimes I am too lazy to peel them before adding to a stew. as long as they're rinsed off i think its OK.
I think it is ok, please rinse well.
Peeling carrots actually removes a great proportion of some nutrients, as they are mainly located just under the surface. I have a good veggie scrubber to remove dirt, and that all I ever use.
And those "baby" carrots are actually just the nubs of real carrots that have had the outer parts removed. Probably because they were going bad. Real baby carrots are carrot-shaped, just smaller, a little hairy and very delicious. The travesty they pass off in the bags as "baby" carrots I find tasteless and spongy or woody. I've totally boycotted them.
Eat your whole carrots proudly! Power to the unpeeled!!
Sometimes I peel, sometimes I don't.
I agree completely with victoriagirl that baby carrots are pretty nasty.
Another interesting tidbit about carrots. Evidently, if you cook them, they will retain more vitamins if they are cooked whole, and then cut up after cooking. Link.
Use a vegetable brush and scrub to make sure they are clean. That goes for potatoes and other vegetables with a thin skin. Personally, I don't like the taste of carrot skin so I peel mine.