3. The number of zeros of the function $f(x)=x^{2} \ln x+x^{2}-2$ is . $\qquad$
3.1 .

From the condition, we have
$$
f^{\prime}(x)=2 x \ln x+x+2 x=x(2 \ln x+3) \text {. }
$$

When $0\mathrm{e}^{-\frac{3}{2}}$, $f^{\prime}(x)>0$.
Thus, $f(x)$ is a decreasing function on the interval $\left(0, \mathrm{e}^{-\frac{3}{2}}\right)$ and an increasing function on the interval $\left(\mathrm{e}^{-\frac{3}{2}},+\infty\right)$.
Also, $00 .
\end{array}
$$

Therefore, the number of zeros of the function $f(x)$ is 1.