May be I am missing something here, but the upper bound on the srqrt(x) for any positive integer x cannot be more that x/2 (in fact its x/2 ONLY for number from 48) for any integer > 8, the upper bound on the sqrt is strictly < x/2. So that makes me wonder  why are so many folks taking such a huge upper bound (INT_MX) for this problem ?
Why are people taking INT_MAX as the upper bound in the binary search approach ?


here is one example : https://oj.leetcode.com/discuss/11508/myolgint_maxsolutionusingbinarysearch