Final answer:
The room in the hospital that staff must enter only wearing protective clothing is the Operating room.
Step-by-step explanation:
The room in the hospital that must be kept free of dust and pet hair, and entered only by staff wearing protective clothing is the Operating room. The Operating room is a highly sterile environment where surgeries are performed. To prevent contamination and the risk of infection, it is essential to maintain a clean and controlled environment in the Operating room.