Answer: Gardening is especially difficult when feeder roots grow above and just barely below the surface of the soil. Any bed that you create will be invaded by roots seeking moisture and nutrients, and the competition to whatever you plant there will probably be too much for the new plants.
Trying to grow grass under trees with surface roots is just as difficult a task. Not only is the lumpy terrain difficult to mow, but the grass has to contend with competition for water and minerals, plus the added grief of too much shade.
Some groundcovers, vinca minor is a good example, will grow happily under such circumstances, and may be a better choice for growing under your ash. Or, you may opt to cover the entire area with an attractive mulch material like bark chips or colored gravel. If you place a thick layer, you'll suppress weeds, as well as making the area under your tree look attractive.
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