# Get to the root of the problem

Calculus Level 4

$\large \begin{cases} f(x)=\sqrt{\frac{x}{\sqrt[3]{\frac{x}{\sqrt[4]{\frac{x}{\ddots}}}}}} \\ g(x)=\sqrt{x\sqrt[3]{x\sqrt[4]{x\sqrt[5]{\cdots}}}} \end{cases}$

The functions $$f(x)$$ and $$g(x)$$ are defined for positive real numbers $$x$$ as above. What is the value of $$y$$ for which $$f(y)g(y)=2016$$?

Give your answer as $$\lfloor y \rfloor$$.

Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

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