# Extreme Rationalizing!

Algebra Level 5

$\large\dfrac{\sqrt{\color{#20A900}{10}\color{#3D99F6}+\sqrt{1}}\color{#3D99F6}+\sqrt{\color{#20A900}{10}\color{#3D99F6}+\sqrt{2}}\color{#3D99F6}+\cdots\color{#3D99F6}+\sqrt{\color{#20A900}{10}\color{#3D99F6}+\sqrt{99}}}{\sqrt{\color{#20A900}{10}\color{#69047E}-\sqrt{1}}\color{#3D99F6}+\sqrt{\color{#20A900}{10}\color{#69047E}-\sqrt{2}}\color{#3D99F6}+\cdots\color{#3D99F6}+\sqrt{\color{#20A900}{10}\color{#69047E}-\sqrt{99}}}$

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

×

Problem Loading...

Note Loading...

Set Loading...