3. The number of zeros of the function $f(x)=x^{2} \ln x+x^{2}-2$ is

The translation is provided while preserving the original text's line breaks and format.
Let $t=x^{2}, g(t)=\frac{1}{2} t \ln t+t-2, g^{\prime}(t)=\frac{1}{2}(\ln t+1)+1=\frac{1}{2}(\ln t+3)$, then $g(t)$ is monotonically decreasing on $\left(0, \mathrm{e}^{-3}\right)$ and monotonically increasing on $\left(\mathrm{e}^{-3},+\infty\right)$, and $g(0)0$, so $f(x)$ has 1 zero point in $(0,+\infty)$.