Paul spoke to them in Hebrew not Aramaic, Acts 21:40
Saw on a friend's post that the Greek word "Hebrais" at Acts 21:40 and elsewhere, really means Aramaic contrary to its obvious similarity to the word Hebrew and dissimilarity to the Greek word for Aramaic, "Syristi."
(For "Syristi" being the Greek word for Aramaic, see the LXX of Daniel 2:4 for "syristi", available here http://studybible.info/interlinear/Daniel%202:4 then compare how that passage is translated as "Aramaic" in all the modern Bibles here http://bible.cc/daniel/2-4.htm )
Anyway contrary to all the lexicons, which acknowledge that "Hebrais" means Hebrew, but then add, without evidence of any kind, that it must mean Aramaic, it does in fact mean Hebrew. Here's a link to a nice discussion of that point on the Biblical Greek mailing list:
As for Hebrew being irrelevant to study of the New Testament because the NT was written in Greek please see all the Hebrew scriptures quoted by the writers of the New Testament.
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