Are there any limitations to a proof of contradiction?
For eg: Proving $p\sqrt q$ rational, given that $p$ is rational and $\sqrt q$ is irrational.
We go by the usual technique of contradiction and assume it to be rational.
But it becomes rational if it is squared. So we can't go on proving it irrational if we square it before.
Why this problem? Where is the flaw and where did I go wrong?
Not sure I understand your question right. But generally proof by contradiction is 'more powerful' than direct proofs. i.e. there are statements which can be proven by contradiction but not in a direct manner. However direct proofs are considered to be more useful, since they contain more information e.g. in the form of computational content which can be extracted to turn the proof into an algorithm.