How to calculate y value from ((y*y) mod prime) efficiently i am working ECC-224 bit. can any one tell me, how to calculate y value from ((y*y) mod prime) efficiently for large bit numbers.
By "ECC-224", I suppose that you mean "NIST curve P-224". This actually matters.

To compute the square root of $z$ modulo a prime $p$, there are several methods which depend on $p$. If $p = 3 \pmod 4$ then it suffices to compute:

$$ y = z^{(p+1)/4} \pmod p$$

If $z$ is indeed a square, this will yield a value $y$, and the other square root will be $-y$ (to check whether $z$ is really a square, just compute $y^2 \pmod p$ and see if it yields back your value $z$ or not).

Now, in NIST curve P-224, computations are done modulo a prime $p$ which is such that $p = 1 \pmod 4$, and the method above does not work. You have to use Tonelli-Shanks algorithm which is slightly more complex, and, in the general case, requires knowledge of a value modulo $p$ which is not a square (half o values modulo $p$ are not squares, so finding one is not hard, but this is enough to make the algorithm, in all generality, probabilistic).