Why isn't it y^4?

Algebra Level 5

\[\displaystyle\sqrt{xy} +\sqrt{yz} +\sqrt{xz} +x^4+y^3+z^4\]

What is the minimum value of the above expression if \(xyz=2\)? Give your answer to 1 decimal place.

Clarification: Yes, it's \(y^3 \) and not \(y^4 \).

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