Closed form

Let $\xi =\sqrt[16]{4870847-\frac{1}{4870847-\frac{1}{4870847-\frac{1}{4870847-\dots }}}}$

$\xi$ can be written $\frac{a+\sqrt{b}}{c}$ for some coprime integers a,b,c.

Can you find them?

Answer format: a,b,c