cryptography FACTORING?

Suppose you discover that
880525^2 ≡ 2, 2057202^2 ≡ 3, 648581^2 ≡ 6,
668676^2 ≡ 77, all modulo 2288233.

How would you use this information to factor 2288233? Explain fully the steps that you would do, but
you do not need to actually perform the numerical computations.


What method should I use?
I think using Fermat factorization method is not a good idea, it takes too long to find out the answer.