Given that:

   1              1
------------- - -----
√(22-10-2022)    √(22)

= 0.00....00ABCD...(N zeros).
Accordingly, exactly N zeros immediately follow after the decimal point, and:
ABCD are base 10 digits, whether same or different, with A being nonzero.

Determine the value of N.

*** As an extra challenge, solve this puzzle without using computer program or excel solver.