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[tex]on \ pose \ n=2010[/tex]
[tex]\sqrt{2008 \sqrt{2009 \times 2011+1}+1} \\ =\sqrt{(n-2) \sqrt{(n-1) \times (n+1)+1}+1} \\ =\sqrt{(n-2) \sqrt{n^2-1+1}+1} \\ =\sqrt{(n-2) \sqrt{n^2}+1} \\ =\sqrt{(n-2) \times n+1} \\ =\sqrt{n^2-2n+1} \\ =\sqrt{(n-1)^2} \\ =n-1 \\ =2009[/tex]