The sprout (the above ground bit) comes quite a bit before the roots -- the roots actually emerge from the stem itself after it has grown quite tall, not from t

The sprout (the above ground bit) comes quite a bit before the roots -- the roots actually emerge from the stem itself after it has grown quite tall, not from the potato itself. "Sprouted potatoes" refers to this initial stem starting to emerge. You've almost certainly been eating potatoes with the above-ground bit growing. They do look a bit like roots. But, really, it's not that poisonous unless the potato itself is also bright green.