**Core Concept**
Adenoidectomy with grommet insertion is the treatment of choice for a child presenting with recurrent upper airway infections (UI), mouth breathing, failure to thrive, high-arched palate, and impaired hearing. This condition is characteristic of adenotonsillar hypertrophy, which is a common cause of upper airway obstruction in children.

**Why the Correct Answer is Right**
The child's symptoms are indicative of adenotonsillar hypertrophy, which is causing upper airway obstruction. Adenoidectomy is a surgical procedure aimed at removing the adenoids, which are a mass of lymphoid tissue located in the nasopharynx. The adenoids play a crucial role in the development of the nasal and oral cavities, and their hypertrophy can lead to nasal congestion, mouth breathing, and impaired hearing due to Eustachian tube dysfunction. Grommet insertion is a procedure used to treat middle ear effusion and impaired hearing by allowing air to enter the middle ear and draining fluid. The combination of adenoidectomy and grommet insertion is essential to address both the upper airway obstruction and the middle ear effusion.

**Why Each Wrong Option is Incorrect**
**Option A:** Tonsillectomy alone may not be sufficient to address the upper airway obstruction caused by adenotonsillar hypertrophy, as it only removes the tonsils and not the adenoids.

**Option B:** Grommet insertion alone may not be sufficient to address the upper airway obstruction and impaired hearing caused by adenotonsillar hypertrophy, as it only treats the middle ear effusion and not the underlying cause of the obstruction.

**Option C:** Myringotomy with grommet insertion is a procedure used to treat acute otitis media or middle ear effusion, but it does not address the upper airway obstruction caused by adenotonsillar hypertrophy.

**Clinical Pearl / High-Yield Fact**
It is essential to diagnose and treat adenotonsillar hypertrophy in children to prevent long-term consequences such as speech and language disorders, hearing loss, and dental malocclusion.

**✓ Correct Answer: D. Adenoidectomy with grommet insertion. Adenoidectomy with grommet insertion is the definitive treatment for adenotonsillar hypertrophy in children.**