# algorithms – Computing square vs computing square-root? Time complexity

I am working on something that requires checking a very large natural number $$x$$ to determine if it is the square root of an even larger natural number $$y$$. So I am wondering what are the fastest algorithms for computing square and square root, and how should I be approaching this i.e.

1. Computing $$sqrt{y}$$ and comparing it with $$x$$
OR
2. Computing $$x^2$$ and comparing it with $$y$$

So as to write a code that has minimum time complexity.