Final answer:
The oculomotor, trochlear, and abducens nerves, corresponding to the third, fourth, and sixth cranial nerves, are responsible for controlling the muscles that move the eyeball.
Step-by-step explanation:
The cranial nerves that control the muscles that move the eyeball are the oculomotor, trochlear, and abducens nerves, which correspond to the third, fourth, and sixth cranial nerves respectively. These nerves are responsible for coordinating the movements of the eye and are essential in tracking and locating visual stimuli. For instance, the abducens nerve exclusively controls the lateral rectus muscle to abduct the eye whereas the trochlear nerve innervates the superior oblique muscle to rotate the eye. Conversely, the oculomotor nerve has the broadest role, controlling all other extraocular muscles, including the muscle that lifts the upper eyelid.