Peel and finely shred celery root and potatoes together into a large mixing bowl. Stir in olive oil, eggs, garlic, and salt. Using 1/3 cup mixture for each latke, press mixture into patties about the size of the palm of your hand, squeezing out excess liquid.
In a large skillet heat oil over medium-high heat. Carefully slide patties into hot oil. Cook over medium-high heat about 2 minutes or until latkes are golden brown, turning once.
Repeat with remaining batter. Add additional oil during cooking, as needed. If necessary, reduce heat to medium to prevent overbrowning. Drain on paper towels and keep warm. Serve with sour cream or apple sauce, if desired.
Makes about 10 latkes. Nutrition information is given per latke with 1 teaspoon of sour cream.