Has anyone tried (successfully) to grow root ginger from root ginger?

I had a small piece of root ginger that was beginning to sprout, so after soaking it overnight, put it in a small pot of compost. I kept this on my sunny kitchen window sill and gave it all the TLC that I could think of. That was about three months ago - I now have a lovely looking plant, very green and healthy, but as the roots were beginning to poke through the bottom of the pot, decided to re-pot it. I was full of anticipation as to what I might find under the soil ............ and was very sad just to find a load of thread-like roots - no resemblance to root ginger??!! Am I being impatient, does root ginger only form from a plant the size of a tree??! Any advice would be much appreciated!