Can bnfinit recognize square integer factors without factorization?

Version 2.11.1

after several allocatemem()s:

? setrand(1);L=2^30;p=randomprime(L);q=randomprime(L);
n=p^2*q;addprimes(n);K=bnfinit(x^2+n);

Takes very long, didn't wait it to finish.

Can this be used as algorithm to recognize square integer factors?

bonus points if bnfcertify() passes :)

CC'me, don't read the list often.