This can't be pretty

Algebra Level 3

\(\dfrac{1}{\sqrt{3+2\sqrt{2}}}+\dfrac{1}{\sqrt{5+2\sqrt{6}}}+\dfrac{1}{\sqrt{7+2\sqrt{12}}}+\dfrac{1}{\sqrt{9+2\sqrt{20}}}+...\)

\(+\dfrac{1}{\sqrt{197+2\sqrt{9702}}}+\dfrac{1}{\sqrt{199+2\sqrt{9900}}} = \ ? \)

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