Get rid of Ridiculous Radicals!

Number Theory Level pending

\[\sqrt { x\sqrt { y\sqrt { z } } } =\quad 8 \quad and \quad \sqrt{x} = \sqrt{\sqrt{y}} = \sqrt{\sqrt{\sqrt{z}}} \quad \Rightarrow \quad x+y+z\quad =\quad ?\quad \] Note: \(\text{ x, y and z are non-negative integers}\)

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