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Algebra Level 3

1100+99+199+98+198+97++13+2+12+1\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 kk, find k2k^{2}.

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