# Extreme Rationalizing!

**Algebra**Level 5

\[\large\dfrac{\sqrt{\color{green}{10}\color{blue}+\sqrt{1}}\color{blue}+\sqrt{\color{green}{10}\color{blue}+\sqrt{2}}\color{blue}+\cdots\color{blue}+\sqrt{\color{green}{10}\color{blue}+\sqrt{99}}}{\sqrt{\color{green}{10}\color{purple}-\sqrt{1}}\color{blue}+\sqrt{\color{green}{10}\color{purple}-\sqrt{2}}\color{blue}+\cdots\color{blue}+\sqrt{\color{green}{10}\color{purple}-\sqrt{99}}} \]

If the expression above equals to \( a+\sqrt{b} \) for positive integers \(a\) and \(b\), find \(a+b\).

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