A thin, uniform, rectangular plate of mass 2 kg is placed in the $x$-$y$ plane as shown in the figure. The moment of inertia about the $x$-axis is $I_x = 0.2 \, \text{kg m}^2$ and the moment of inertia about the $y$-axis is $I_y = 0.3 \, \text{kg m}^2$. The radius of gyration of the plate about the axis passing through $O$ and perpendicular to the plane of the plate is: