Pandigital numbers (squares)

Hello everybody!

I need a little help with my homework. I need to find all (natural) numbers whose squares are pandigital numbers (they use each of the digits 0,1,...,9 *only once*), e.g. .

Since that would take ages to do manually, I made a small program in Mathematica which finds all such numbers. Now, I would like to know if there is some "more mathematical" way to do this or is it simply the work for computers.

Just a few tips, please! Thanks in advance.

P.S. Sorry for eventually bad English. It's not my native language.