Integer solutions for $n$ for $|{\sqrt{n} - \sqrt{2011}}| < 1$ $$|{\sqrt{n} - \sqrt{2011}}| < 1$$
What is the number of positive integer $n$ values, which satisfy the above inequality.
My effort:
$ 
({\sqrt{n} - \sqrt{2011}})^2 < 1 \\n + 2011 -2\sqrt{2011n} < 1\\ n+2010<2\sqrt{2011n}\\ n^2+2 \times 2010 \times n +2010^2<4 \times 2011n  \\n^2 -4024n +2010^2 < 0 $  
But it seems this won't lead me for desired answer.

$|\sqrt n - \sqrt{2011}| <1 \iff -1 < \sqrt n - \sqrt {2011 }< 1 \iff 
\sqrt{2011} - 1 <\sqrt n < \sqrt {2011} + 1 \iff (\sqrt{2011} - 1)^2 < n < (\sqrt{2011}+1)^2.$  You should be able to finish it from here.
