Which nerve would the dentist need to anesthetize to work on that tooth?

Inferior alveolar - The inferior alveolar nerve is a branch of the mandibular division of the trigeminal nerve (v3). It penetrates the mandibular foramen and is the sensory nerve for the mandible and all mandibular teeth. This is the nerve anesthetized by dentists working on the mandibular teeth. It is anesthetized near the mandibular foramen, so sensory nerves from branches distal to that point would be blocked. The lingual nerve is another branch of v3.It transmits general sensation from the tongue. The lingual nerve also receives the chorda tympani, a branch of the facial nerve.