# 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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