This is the 4074th most frequent Korean word.
자고
"자고" means "sleeping" or "let's sleep," depending on context.
Here, '자고' is used to suggest doing something together in the subjunctive mood.
친구가 영화를 보자고 제안했어요.
A friend suggested that we watch a movie.
In this case, '자고' is part of the verb for sleeping (자다) in its -고 connective form, linking actions.
밤이 늦었으니 이제 자고 내일 일찍 일어나자.
Since it's late at night, let's now sleep and wake up early tomorrow.
Here, '자라고' is derived from '자라다' (to grow) in a secondary meaning indicating assertion or claim in a noun clause context.