Learn Russian: Учитель заулыбался, когда студент ответил правильно. - The teacher broke into a smile when the student answered correctly.

In this lesson, the prefix за- adds the meaning of a sudden, spontaneous start to an action. While the base verb улыбаться means to smile, заулыбался means the teacher suddenly broke into a smile.

Could I just say начал улыбаться instead of заулыбался?

Yes, it is grammatically correct, but заулыбался is much more natural here. It captures the involuntary, quick reaction of breaking into a smile, whereas начал улыбаться (started to smile) sounds a bit more deliberate.

Both заулыбался and ответил are perfective verbs. How do we know which action happened first?

When a sentence has multiple perfective verbs in the past tense, they usually describe a sequence of completed events. Even though the teacher's reaction is written first, the word когда (when) links them so we know the student answered first (ответил), and the smile (заулыбался) was the immediate reaction.

Why does заулыбался end in -ся if the teacher isn't doing an action to himself?

The base verb улыбаться (to smile) is a naturally reflexive verb in Russian, meaning it always requires the -ся or -сь ending, even though it doesn't mean doing something to oneself. When we add the prefix за- to change the aspect, the verb keeps its reflexive ending.