How do you kill tree roots?
Make downward cuts in the bark of the sprouts but leave them
intact. Pour some concentrated Roundup into the cuts. Do this for
each sprout. It may take a few attempts.
The only way to make sure no more sprouts come up is to remove
the stump that has been left. The root system below will always try
to send up new sprouts, unless you completely remove the stump and
roots. The above answer may work.