If a girl goes out with you does this mean she likes you?

It depends on what you mean by "go out".

On a literal level... if she goes out with you as far as to eat or out to the movies, chances are she is at least interested in you in some way shape or form. Majority of the time if a girl is interested in you, she likes you as well.

Others say "go out" as if you both are together. If someone ask how are the both of you and her reply is you both go out or "we go out" then obviously she more than likes you.