# 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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