Given Heidegger's view of Greek philosophy, and in particular the Pre-Sokratics, as in some ways closer to the unhiddeness of being, one would assume that he was using radical in the sense of returning to the root of questioning ("the call to which Western-European thinking is subject, the thinking whose roads we,too, follow as soon as we let ourselves get involved in thinking." (What is Called Thinking?, Part II, Lecture V), at least in the context of the history of philosophy.
Perhaps for Heidegger, a radical approach was at the same time, then, a "going out" in the sense that it requires a new rethinking
of being by returning to the origin of thought itself. It is his contention, we are reminded, that Nietzsche was the last philosopher, because he exhausted in his own thinking Western philosophy in such a way as to bring it to a conclusion. And perhaps, Heidegger's radicalism can be seen as a return to the "fundamental" questions of philosophy that began to be asked by the early Greek philosophers.