No, it is not required. Part of it depends on how impacted the molar is (how much bone is over the tooth and how difficult the dentist expects the removal to be). Also, it depends on how nervous the patient is. A simple extraction could be done with just a local anesthetic. Some times some medication can be given I.V. to sedate the patient (twilight sleep). Occasionally nitrous oxide (laughing gas) can be administered. A general anesthetic would be administered for a particularly difficult case or if the dentist or patient didn't think the patient could tolerate the procedure with the options mentioned earlier. Some people confuse sedation or twilight sleep with general anesthesia. From the patient's perspective, they don't remember anything so they think they were asleep with a general anesthetic. Physiologically, they are not under general anesthesia with sedation. Sedation is like a light dimmer switch. The light gets dimmer and dimmer (sedation) until the light goes out (general anesthesia).