$\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}$
$\frac{\sqrt2+\sqrt3+\sqrt6+\sqrt8+\sqrt16}{\sqrt2+\sqrt3+\sqrt4}$

$=\frac{\sqrt2+\sqrt3+\sqrt6+\sqrt8+4}{\sqrt2+\sqrt3+\sqrt4}$

$=\frac{\sqrt2+\sqrt3+2+2+\sqrt6+\sqrt8}{\sqrt2+\sqrt3+\sqrt4}$

$=\frac{(\sqrt2+\sqrt3+\sqrt4)+(\sqrt4+\sqrt6+\sqrt8)}{\sqrt2+\sqrt3+\sqrt4}$

$=1+\sqrt2$

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