For $x$, $y$, and $z$ positive real numbers, what is the maximum possible value for\[\sqrt{\frac{3x 4y}{6x 5y 4z}} \sqrt{\frac{y 2z}{6x 5y 4z}} \sqrt{\frac{2z 3x}{6x 5y 4z}}

Infinity

Step-by-step explanation:

Since x,y,z are positive rel numbers, we have that

Hence,

Now let

if we take x=y=1, we have

and so f(1,1,z) tends to infinity as z goes to 0.

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