Normally when taking square root of $x$ modulo $a$, $a = p*q$, where $p$ and $q$ are primes, you would compute $$\sqrt{x} \pmod p$$ $$\sqrt{x} \pmod q$$ and then use the Chinese Remainder Theorem to compute $$\sqrt{x} \pmod {pq}$$
This method would work for example when $a = 143$, and $p=13, q = 11$. However, what approach would I use when $a = 121$? $p=q=11$, and I won't be able to use CRT because $\sqrt{x} \pmod p == \sqrt{x} \pmod q$. I could probably do it by hand, but is there a better approach that doesn't involves that?
