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The inner floor is redundant
If the inner floor were not redundant, then we would expect that floor(sqrt(n)) != floor(sqrt(m)), where m = floor(n)
note that n - 1 < m <= n. m is always less than or equal to n
floor(sqrt(n)) != floor(sqrt(m)) requires that the values of sqrt(n) and sqrt(m) differ by at least 1.0
however, there are no values n for which the sqrt(n) differs by at least 1.0 from sqrt(n + 1), since for all values between 0 and 1 the sqrt of that value is < 1 by definition.
thus, for all values n, the floor(sqrt(n)) == floor(sqrt(n + 1)). This is in contradiction to the original assumption.
Thus the inner floor is redundant.