word choice - Can "real" be used as an adverb to describe an adjective?

Is this correct?

That is a real cool answer.

I learned that that was incorrect, since "real" is an adjective which can describe a noun, e.g. "real answer" but it is not an adverb which can describe an adjective, "real cool". Instead you would have to say:

That is a really cool answer.

Since "really" is an adverb.