Slice the beets and the sweet potatoes 1 mm thick with a mandoline. Shave the carrots with a vegetable peeler. Shave one side until you reach the core and then flip the carrot over and shave the other side.
Set up three bowls of ice water and let the vegetable rest in the water for 30 minutes.
While the vegetables are resting, add the oil to a heavy, high side pot and heat it to 350F as read with a high temperature thermometer. I heat the oil on low to medium low and it takes 15-20 minutes on my stove.
Drain each type of vegetable and blot them dry with towels. The drier the better for frying.
Set up two cooling racks lined with paper towels.
For the beets and sweet potatoes, fry them for 4 minutes, turning frequently until they are browned and crisp. This will take 5 batches. As you remove each batch to the cooling rack with your skimmer, sprinkle it with some salt and spread it out to drain. Then, when you're ready to scoop out the next batch, pile them up on the other cooling rack.
For the carrots, fry them for 2-3 minutes. Keep a close watch so they don't burn. Transfer them to the cooling rack as before and sprinkle with salt. Three carrots are 2 batches for the fryer.
Fresh vegetable chips don't last long. Eat them preferably as soon as they come out of the fryer, and definitely within 2 hours of frying.