Question
The previous owner of my home had liquid amber trees in the front yard.  They removed them before I purchased the home because the roots had pushed up the driveway.  There are still many shoots appearing.  I have sprayed the shoots with roundup and they are dying.  My big concern is that the roots do not continue to grow so that they might impact the foundation.  I was planning to dig up the roots and put root killer on anything I can't dig out.  Is this the proper course of action?  Any other recommendations to make sure I kill these roots? There are no visible stumps to grind.

Answer
if you sprayed the sprouts with Roundup and they are dying just let them die and do not cut them off until the leaves have dries out (wait about 2 weeks after the leaves start to die). The Roundup will be carried down to the root system and kill the roots. If you cut the sprouts as soon as they seem to be dying this may stop the movement to the roots. The use of  herbicides is an alternative to digging the roots up so let the herbicide do its thing.
You may get more sprouts from other roots so just spray them as them appear and this will take care of the root problem.