If you're willing to tolerate an intersection function which has the
possibility of error, it seems like just using bounding squares instead
of bounding circles would give better error bounds if you expect your
circles to often be of very different sizes.
With regard to the actual question you asked, I can't think of a good
way without square roots off of the top of my head, but if you're
willing to tolerate a bit of approximation error then computing them
needn't be slow:
http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Approximations_that_depend_on_IEEE_representation
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