Final answer:
To anesthetize the patient for the extraction of the non-restorable tooth, you would need to anesthetize the inferior alveolar nerve, posterior superior alveolar nerve, and anterior superior alveolar nerve.
Step-by-step explanation:
In this case, to anesthetize the patient for the extraction of the non-restorable tooth, you would need to anesthetize the following nerves:
- Inferior alveolar nerve: This nerve supplies the mandibular teeth and their surrounding tissues, making it necessary to numb the lower teeth prior to dental work.
- Posterior superior alveolar nerve: This nerve supplies the maxillary molars, including the upper left maxillary tooth with the large cavity.
- Anterior superior alveolar nerve: This nerve supplies the maxillary incisors and canines. Although not explicitly mentioned in the case, it may be necessary to anesthetize this nerve as well if any of the adjacent teeth require treatment.