Largest Pandigital Square

Theorem
The largest pandigital square (in the sense where pandigital includes the zero) is $9 \, 814 \, 072 \, 356$:


 * $9 \, 814 \, 072 \, 356 = 99 \, 066^2$

Proof
We check all the squares of numbers from $99 \, 067$ up to $\floor {\sqrt {9 \, 876 \, 543 \, 210} } = 99 \, 380$, with the following constraints:

Since all these squares has $9$ as its leftmost digit, the number cannot end with $3$ or $7$.

The number cannot end with $0$ since its square will end in $00$.

A pandigital number is divisible by $9$, so our number must be divisible by $3$.

These constraints leaves us with the following $74$ candidates:

By inspection, none of these numbers are pandigital.