Is the square root of 3 rational?

No, the square root of 3 is not rational.
No. The square root of 3 is irrational.

More generally: if p is a Prime number then the square root of p is irrational and the proof of this fact mimics the famous proof of irrationality of the square root of 2.
No - the square root of 3 is not rational, but the proof is too involved to post here.