Loosen the soil around the base a little then try and pull it up so it detaches from the main root. That is supposed to reduce the chances of it re-sprouting compared with cutting it off cleanly.
A trowel in the hand is worth a thousand lost under a bush.
Yes, I think they are. Looks like it might be a case of keeping an eye out and pulling them up whenever you see one. Hard pruning or damage of some kind can cause trees to send up suckers from the roots like these, but some trees just seem to make a habit of it, unfortunately.
A trowel in the hand is worth a thousand lost under a bush.
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Mate these also suckers from the plum tree?