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 $x$
  2. Computing $x^2$ and comparing it with $y$

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