Final answer:
The Inferior alveolar nerve is the most at risk during extractions, and damaging it may lead to numbness or loss of sensation in the lower lip, chin, and tongue.
Step-by-step explanation:
The nerve that is most at risk during the extraction is the Inferior alveolar nerve. This nerve is responsible for supplying sensory innervation to the lower teeth and jaw. During a dental extraction, there is a possibility of damaging this nerve, which could result in numbness or loss of sensation in the lower lip, chin, and tongue.