Preheat oven to 200 degrees or "warm" setting. Peel potatoes and submerge in cold water. Peel celery root with a paring knife. Pulse the onion and garlic in food processor. Mixture should be coarse, not completely pureed. Pour onion-garlic mixture into a large bowl.
Grate the celery root using the larger grate of a box grater, or use the grater attachment of a food processor. Add to onion-garlic mixture and stir.
Grate potatoes. Quickly squeeze a handful of grated potatoes at a time over a second bowl (or the kitchen sink) to remove all liquid. Add the dry potatoes to the onions and celery root, mixing as you go. This step should be done as quickly as possible to prevent oxidation of the potatoes.
Heat 1/4 inch of olive oil in a large, heavy skillet (cast iron works best) over medium-high heat, until just below the smoking point.
Add remaining ingredients to the batter, and stir until fully combined. Place a small handful of batter (approximately 1/4 cup) in the hot oil at a time. Pat each handful into a 1/2" thick pancake shape before placing in oil - This will help each latke stay together. Fry until completely golden-brown on the bottom and crispy around the outside corners. Flip and brown on the second side.
Transfer latkes to a plate lined with paper towels or several layers of brown paper (I use grocery bags). Allow paper to absorb excess oil, then transfer latkes to a cooking rack placed over baking sheet in the preheated oven, where they will stay warm until ready to serve. Serve hot, with sour cream and applesauce.
Extra latkes can be frozen on a baking sheet in the freezer, with parchment paper between the layers. When frozen, transfer to ziploc bags. Reheat in oven at 400 degrees F.