In a blender or food processor, process the ginger and 1/2 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 1/4 cup of water. Puree again, it shouldn't need as long and strain again. Do this one more time with another 1/4 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.