It's Mehul's birthday

Algebra Level 3

\[\begin{align} \sqrt{x}+\sqrt{y}+\sqrt{z}&=4 \\ x^2 +y^2 +z^2&=40.125 \\ e^{xyz}&=4.771\end{align}\]

Find \(x+y+z\)


This problem is dedicated to Mehul Arora on his birthday. This problem is not an original.
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