Distribution of square numbers in intervale

Question

The square numbers are of the form $n^{2}$ $(1,4,9,16,...)$

My question is there some formula to know how many square numbers up to $x$? or a least approximation formula ?

Answer 1

If $n^2\le x<(n+1)^2$, then $n\le \sqrt x\lt n+1$, which means $n=\lfloor\sqrt x \rfloor$,

where $\lfloor y\rfloor$ is the greatest integer part of $y$.