I have a sweetgum tree in my yard that has a large root growing basically on top of the ground extending towards my sidewalk and house. If I remove this root will I cause any damage to the tree?

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Never argue with idiots....... They will drag you down to their level and then beat you with experience!

Yes. Removing a root that size could kill the tree quite handily.

Has the exposed part in fact gotten any closer to the house or walk as you have observed it growing?

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Shepherd of the Trees
It is not our part to master all the tides of the world, but to do what is in us for the succor of those years wherein we are set, uprooting the evil in the fields we know so that those who live after may have clean earth to till.