Dig it carefully (try not to break up the white roots) and pick out all the bits. Do it again in another couple of weeks and you'll find more that you missed first time round.
The point of doing this is to make less plant to kill.
Let any stems grow, encourage them up canes or sticks to make them easy to handle and keep them out of things you want.
Once they reach a good length,with some full leaves, carefully coil them up (still attached to the root), put some rubber gloves on and wet them liberally with a systemic weedkiller* and seal them in a plastic bag with a rubber band round the neck.
Let them 'stew' for a while to let the chemicals kill the root.
"Weedol" do some strong products – they will neutralise on contact with soil so you can replant quickly.
Be careful to observe safety precautions and don't get the Weedol on anything you want to keep, even splashes of it..
Repeat until defeated.