Why isn't it y^4?

Algebra Level 5

xy+yz+xz+x4+y3+z4\displaystyle\sqrt{xy} +\sqrt{yz} +\sqrt{xz} +x^4+y^3+z^4

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

Clarification: Yes, it's y3y^3 and not y4y^4 .

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