I suppose by scholarly standards we don't know that any Babylonians knew this method (the first of whom we're sure would be a 1st century Greek mathematician),

I suppose by scholarly standards we don't know that any Babylonians knew this method (the first of whom we're sure would be a 1st century Greek mathematician), and the result on the stone is generally attributed to an unknown source (wikipedia). But I guess you could call the attribution folk knowledge, I have often seen this method called something like Babylonian root-finding.