Radioactive iodine therapy is the most appropriate management for a solitary toxic thyroid nodule because it effectively destroys hyperfunctioning thyroid tissue while preserving normal thyroid tissue, leading to resolution of hyperthyroidism. Unlike antithyroid drugs, which only provide temporary control, radioactive iodine offers a definitive, non-invasive treatment. Surgery is reserved for large nodules causing compressive symptoms or suspicion of malignancy. Observation alone is inappropriate due to the risk of worsening thyrotoxicosis. Thus, radioactive iodine balances efficacy, safety, and patient comfort in most cases.

Reference: Harrison's Principles of Internal Medicine, 20th Edition.