Pandigital Pairs whose Squares are Pandigital

Theorem
The elements of the following pandigital pairs of integers each have squares which are themselves pandigital:
 * $\left({35 \, 172, 60 \, 984}\right), \left({57 \, 321, 60 \, 984}\right), \left({58 \, 413, 96 \, 702}\right), \left({59 \, 403, 76 \, 182}\right)$