That's plenty. The root only needs to stick out 1/4" before planting, and even that isn't completely necessary since you can plant seeds with no roots sticking out at all and still have some grow. It may depend on your technique and how much root you need for it, but that can be planted in seed starter soil with the root covered in dirt, in a plastic cup with a piece of plastic wrap rubber-banded over it. Poke two finger-sized holes in the wrap for air and place under fluorescents. The plastic wrap will keep up the humidity until the root grows further and the plant stands up.
Always keep the amount of light that touches roots to an absolute minimum. Check sprouting seeds in dim light and quickly re-cover, keep the paper towel in the dark, etc.