Squares of 23...3

Theorem

The following pattern holds:

$\ds 3^2$

$=$

$\ds 9$

$\ds 23^2$

$=$

$\ds 529$

$\ds 233^2$

$=$

$\ds 54 \, 289$

$\ds 2333^2$

$=$

$\ds 5 \, 442 \, 889$

$\ds 23333^2$

$=$

$\ds 544 \, 428 \, 889$

and so on.

Proof

This theorem requires a proof.
In particular: Simple but tedious.
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Sources

1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2333$
1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2333$