Number whose Square is in 2 Identical Halves

Theorem
The number $36 \, 363 \, 636 \, 364$ has the property that its square can be split into two identical halves:
 * $36 \, 363 \, 636 \, 364 = 1 \, 322 \, 314 \, 049 \, 613 \, 223 \, 140 \, 496$

Proof
It just does.