In a large saute pan, combine the carrots, 1/2 cup of the water, and butter. Sprinkle the sugar over the top and bring to a boil over medium-high heat Cover and reduce the heat to medium. Simmer for 10 minutes, or until the carrots are almost tender.
Add the celery root (add more water if the mixture is dry). Cook for 5 minutes, or until the celery root is just tender.