Difficult system of equations

Algebra Level 4

\[ \begin{array} { l l l l l l l l l } x & + & y & + & \sqrt{z} & = & 148 \\ x & + & \sqrt{y} & + & z & = & 82 \\ \sqrt{x} & + & y & + & z & = & 98 \\ \end{array} \]

Find the value of \( x + y + z \).

Note: \(x, y, z \) are positive integers.


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