Can it be summed up?

i offer you this $|\sqrt{a}-\sqrt{b}|=\sqrt{c-2\sqrt{d}}\Longrightarrow a+b-2\sqrt{ab}=c-2\sqrt{d}$ $a+b=c, d=ab$ using this : $\dfrac{1}{\sqrt{n+\sqrt{n^2-1}}}=\dfrac{\sqrt{n-\sqrt{n^2-1}}}{\sqrt{n+\sqrt{n^2-1}}*\sqrt{n-\sqrt{n^2-1}}}=\sqrt{n-\sqrt{n^2-1}}$ $\sqrt{n-\sqrt{n^2-1}}=\dfrac{\sqrt{2n-2\sqrt{n^2-1}}}{\sqrt{2}}=\dfrac{\sqrt{n+1}-\sqrt{n-1}}{\sqrt{2}}$ we put this in the summation and $\dfrac{1}{\sqrt{2}}\sum_{n=1}^{9800} (\sqrt{n+1}-\sqrt{n-1})$ it easily telescopes as $\dfrac{\sqrt{2}}{2}(-\sqrt{1-1}-\sqrt{2-1}+\sqrt{9799+1}+\sqrt{9800+1})=\dfrac{\sqrt{2}}{2}(98+70\sqrt{2})=70+49\sqrt{2}$ $70+49+2=\boxed{121}$