I want to make friends with her.is this correct?i'm so gratful for answering me :)

Question

Answer

Yes, that is correct.
I want to make friends.  I want to be friends with her.  I hope we become friends.  I think she would make a good friend.  I like her, and we could become great friends.

Answer

"I want to make friends with her" is perfectly fine. You are stating a fact.

"I'd like to become friends with her" states a wish. This is polite-sounding, but your original sentence is still grammatically correct (although slightly direct).

Answer

i'd like to become friends with her*

Answer

It's perfect.

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