$8\mathrm{.}12$ For the built$-$up structural steel member shown, calculate the moments of inertia with respect to its $x-x$ and $Y-Y$ centroidal axes.

$8\mathrm{.}25$ Compute the radii of gyration with respect to the $x-x$ and $Y-Y$ centroidal axes for the built$-$up steel member of Problem $8\mathrm{.}12.$