Just for fun:
public static BigInteger sqrt(BigInteger x) {
BigInteger div = BigInteger.ZERO.setBit(x.bitLength()/2);
BigInteger div2 = div;
// Loop until we hit the same value twice in a row, or wind
// up alternating.
for(;;) {
BigInteger y = div.add(x.divide(div)).shiftRight(1);
if (y.equals(div) || y.equals(div2))
return y;
div2 = div;
div = y;
}
}