1) Not all representations of square roots have non-terminating form. Continued fractions, for instance, reach a repetitive cycle. Other irrational functions

1) Not all representations of square roots have non-terminating form. Continued fractions, for instance, reach a repetitive cycle. Other irrational functions have other patterns. 2) No. If you are just doing sums, the cost is O(N) in time and space where N is the total number of bits in the input. If the inputs are large (i.e. N is big) then you have more time to compute the answer.