Potatoes that have sprouted can still be eaten safely if certain conditions are met: the potato should be firm, not green or wrinkled, and the sprouts must be completely removed before cooking or eating. The sprouts and any green parts contain toxins like solanine and chaconine, which can cause symptoms like nausea or stomach cramps if ingested in large amounts. If the potato is soft, shriveled, has long sprouts (more than about half an inch), or green discoloration, it should be discarded as these signs indicate higher toxin levels. Proper storage in a cool, dark, and dry place can help prevent sprouting.

In summary, sprouted potatoes are safe to eat after thoroughly cutting away all sprouts and green areas, while potatoes showing significant spoilage or greening should be thrown out to avoid health risks.