9. Let $n$ be a natural number, for any real numbers $x, y, z$ there is always $\left(x^{2}+y^{2}+z^{2}\right)^{2} \leqslant n\left(x^{4}+y^{4}+z^{4}\right)$, then the minimum value of $n$ is $\qquad$
By the Cauchy-Schwarz inequality, we have $\left(x^{2}+y^{2}+z^{2}\right)^{2} \leqslant 3\left(x^{4}+y^{4}+z^{4}\right) \Rightarrow \frac{\left(x^{2}+y^{2}+z^{2}\right)^{2}}{x^{4}+y^{4}+z^{4}} \leqslant 3$ $\Rightarrow n \geqslant 3$, so the minimum value of $n$ is 3.