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How to remove tree stumps
Dig around the roots.
Use a shovel to dig next to the stump, exposing the roots underneath the surrounding dirt. Move around the circumference of the stump and continue digging until you've exposed all of the largest roots around the tree.
Dig deep on either side of the roots to expose them as much as possible. If the roots seem very large and deep, and it's difficult to completely uncover them, you might want to consider a different root removal method.