Answer: Almost any tree or shrub which has become established in the landscape will have an extensive root system. To positively and immediately remove the last vestages of the root system, it's best to dig all the roots up. If that course of action appears to require a backhoe, you might do well to just keep the sprouts cut down before they can produce leaves. Once leaves appear they begin the process of photosynthesis (transporting energy to the roots). As long as the roots are being fed, they will respond by producing more shoots. Keeping the shoots cut down will starve out the roots and they'll eventually run out of stored energy and be unable to produce new shoots. It's a process that requires vigilance, but it's the most environmentally friendly way of killing an unwanted root system.
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