Add the potatoes, celery root and 1 tablespoon salt to a large saucepan and cover with water. Bring to a boil and cook over medium-high heat until fork tender, about 15 minutes. Drain the potatoes and celery root.
Preheat the oven to 350 degrees F. Grease a 9-by-13-inch baking pan.
Whip together the cream cheese and softened butter in a large bowl with a hand mixer on medium speed until thoroughly blended, about 2 minutes. Add the hot potatoes and celery root slowly, alternating with the half-and-half. Whip until blended. Sprinkle with salt and stir in the horseradish, garlic powder and white pepper.
Pour the potato mixture into the prepared baking pan. Pour the melted butter over the potato mixture. Bake until bubbly and slightly brown, about 45 minutes. Garnish with the chives.