Approximate a Square Root and Clarify the Integer Follow-up

Write a function that computes the square root of a nonnegative number using basic arithmetic and comparisons. Then explain what changes if the input is guaranteed to be an integer. ### Constraints and Clarifications The report does not specify precision, numeric bounds, or whether the integer follow-up changes the output. For the base practice contract, accept a finite nonnegative real input x, do not call a built-in square-root routine, and return a numerical approximation with absolute error at most1e-9*max(1,sqrt(x)). This tolerance is an explicit practice convention. Numeric representation and a portable finite test domain require later console validation; no unreported maximum is invented. Integer input still has a real square root unless the interviewer explicitly asks for floor(sqrt(n)). ### What a Strong Answer Covers A convergent search interval, overflow-aware comparisons, stopping and floating-point stagnation, and complexity in terms of precision. Discuss the distinct integer-floor variant without silently changing the base return value. ### Follow-up Questions - Why is sqrt(2) not an integer even though2 is an integer? - How can an integer-floor implementation compare a candidate square without multiplication overflow?