Radical Radicals

Algebra Level 3

How many positive xx satisfy

x+x+x++xn square roots=1\Large \sqrt{x} + \sqrt{\sqrt{x}} + \sqrt{\sqrt{\sqrt{x}}} + \ldots + \underbrace{\sqrt{\sqrt{\sqrt{\cdots\sqrt{x}}}}}_{n \text{ square roots}}=1

for a given positive integer n?n?

Bonus: What sorts of bounds can you put on these solution(s) in terms of n?n?

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