A centrifuge has an inertia rotation of 7.24 * 10-3 kilogramsm2. How much energy must be supplied to take it from rest to 419 rad / s?

KE = (1/2)(7.24 * 10-3)(419^2)
is this correct.

Yes, that is correct. (1/2) I w^2

I = 7.24 * 10^-3 kilograms m^2 is called the moment of inertia, not the inertia rotation.