In a blender or food processor, process the ginger and ½ cup water for a few minutes until it turns to liquid. Strain the juice into a large bowl. Transfer the ginger pulp back to the blender or food processor and add another ¼ cup of water. Puree again, it shouldn't need as long and strain again. Do this one more time with another ¼ cup of water. Press on the solids with the back of a spoon to get out all the flavor. Discard the solids, pour the ginger liquid back into blender with lime juice and sugar, process for 30 seconds. Use about 2 ounces of the concentrate to 8 ounces of seltzer to make a ginger beer to enjoy on it's own or in a flavorful cocktail. Refrigerate up to 3 weeks. Shake before serving.
