Just Another Easy Radical Problem

$360^{1+\frac12+\frac14+\frac18+\cdots}=360^2$

Let $x$ be equal to the expression in the problem above.

$x=360\sqrt{x}$ $\implies x^2=129600x$ $\implies x=\boxed{129600}$

On an infinitely nested radical like this, the answer would just be $360^2$ , or $129600$ .

And this, my friends, is something I discovered all by myself.