So the thing is I'm kind of confused with these two. There are times when I see "of" after approve sometimes it does not. Which is which? Both looks fine actually.

1.) His father does not approve of his relationship with Nancy.
2.) His father does not approve his relationship with Nancy.

Question

So the thing is I'm kind of confused with these two. There are times when I see "of" after approve sometimes it does not. Which is which? Both looks fine actually.
 
1.) His father does not approve of his relationship with Nancy.
2.) His father does not approve his relationship with Nancy.

Answer

#1 "to approve of" is a synonym of "to agree with"
#2 "to approve" + gerund/verbal noun is a synonym of "to give (one's) permission" + infinitive

I approve of this, I agree with this
I approve this, I give (my) permission to do this

Answer

Form #1 is common and correct.

Form #2 is used when a teacher, a boss, or a government office needs to give permission for something.

For example: "The director of the department approved my request for a construction permit."

Answer

“To approve” is an action like “to approve the building of a new park” might mean someone in the government actually signed off on it so they could start work. But “to approve of” is an opinion like a resident might say “I approve of the new park”.

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