1. What x satisies x^2= 11 (mod 5)?

You can answer that by "brute strength": 1^2= 1, 2^2= 4, 3^2= 9= 4 (mod 5), 4^2= 16= 1 (mod 5) (Aha!).

2. What x satisfies x^2= 11 (mod 7)?

Do the same thing as above.

Now, what is the "Chinese remainder theorem"?