That's basically it:
$$\nabla \times \frac{\vec{r}}{|\vec{r}|} = 0$$

There's some connection with physical significance of curl of vector function. I am currently in Grade 10 but am in a preparatory physics course. Any help would be appreciated.

Here's what I have so far,

\begin{bmatrix} \hat r & \hat \theta & \hat \phi \\ \frac{\partial}{\partial r} & \frac{\partial}{\partial \theta} & \frac{\partial}{\partial \phi} \\ \frac{1}{r^2} & 0 & 0 \\ \end{bmatrix}

which gives me 0 since \begin{equation}\frac{\partial}{\partial \theta}(\frac{1}{r^2}) \end{equation} and \begin{equation}\frac{\partial}{\partial \theta}(\frac{1}{r^2}) \end{equation} are equal to zero. However, I feel this isn't the right method.