# Iterated Roots with Powers

Algebra Level 4

$\sqrt{ 2^1+ \sqrt{ 2^2+ \sqrt{ 2^4 + \sqrt{2^8 + \cdots } } } }$

The value of above expression is in the form $$\phi \sqrt{A}$$, where $$A$$ is an integer. Find $$A$$.

Notation: The symbol $$\phi$$ denotes the golden ratio, $$\phi = \dfrac{1+\sqrt5}2$$.

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