Answer: To some extent the difficulty will depend on the type of shrub you are trying to remove -- a surface rooted azalea for instance would have a very wide yet shallow root system and would be relatively easy to remove entirely. Unfortunately, the best way to eradicate the roots is to dig them out by hand. A slightly more disruptive method is to attach a chain and pull them out using a sturdy truck. A longer term method is to cut the shrubs off at or below ground level and then cover the surface with heavy layers of carboard and mulch to block the light, in effect "smothering" and starving the roots over time. Planting flowers nearby may actually encourage the shrubs to rejuvenate if the extra soil amendments and water intended for the flowers reach their roots. Keep in mind that the feeder roots probably extend well beyond the branch spread of the shrubs so you may need to grub some of these out prior to planting the flowers.
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