Thread: Ring extension problem - is Z[sqrt(10)] a UFD?

Hi,

I am trying to determine whether Z[sqrt(10)] is a unique factorization domain (UFD), and can't seem to do it.
I'd guess that it isn't, since 10 = sqrt(10) * sqrt(10) = 2*5 are seemingly two different factorizations of it, but how do I prove that 2,5 and sqrt(10) are irreducibles?

Is there any better way to do it?