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 ?
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Welcome to Mathematics Stack Exchange. There are approximately $\sqrt x$ – J. W. Tanner Jun 05 '20 at 21:41
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@J.W.Tanner Why how you get this bound what about the error term.?is there a better approximation. – Abdo Jun 05 '20 at 21:47
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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 $y$.
J. W. Tanner
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