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Algebra Level 3

\[\frac{1}{\sqrt{100}+\sqrt{99}}+\frac{1}{\sqrt{99}+\sqrt{98}}+\frac{1}{\sqrt{98}+\sqrt{97}}+\cdots+\frac{1}{\sqrt{3}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{1}}\]

If the above expression equals \(k\), find \(k^{2}\).

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