Inscribe three mutually tangent pink disks of radii $450$, $450$, and $720$ in an uncolored circle $\Omega$ of radius $1200$. In one move, Elmo selects an uncolored region inside $\Omega$ and draws in it the largest possible pink disk. Can Elmo ever draw a disk with a radius that is a perfect square of a rational? Proposed by Ritwin Narra