OP - I'm beginning to believe your thread title...
It almost doesn't matter what tree you have, as long as it isn't an allelopathic (plant that kills other plants) tree like Black Walnut. However, if the tree is a beech:
Quote:
It also casts dense shade and has an extensive network of shallow, fibrous surface roots that make gardening underneath it almost impossible.
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https://en.wikipedia.org/wiki/Fagus_grandifolia
Gardening underneath the tree is "almost impossible" because the beech loves water and will suck up water that even shady grass needs to grow. If you have an irrigation system, you may be able to ameliorate the problem.
What type of grass did you sow and do you have an irrigation system? After all, you DID ask about GRASS...