He didn't say only one mathematical operator, so it means I can use two ones.
And, if you're so smart Anonymous, find a way you can do it using one mathematical operator.
Good luck !
I found two other ways (the second is a little bit tricky, since a 8 is formed by a 0 put atop another 0)
[(0!+0!)(0!+0!)+0!]!=[(1+1)(1+1)+1]!=(4+1)!=5!=120
$$({\sqrt{({\sqrt{{\mathtt{8}}{\mathtt{\,\small\textbf+\,}}{\mathtt{8}}}}){!}{\mathtt{\,\small\textbf+\,}}{\mathtt{0}}{!}}}){!}$$=$$({\sqrt{({\sqrt{{\mathtt{16}}}}){!}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}}}){!}$$=$$({\sqrt{{\mathtt{4}}{!}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}}}){!}$$=$$({\sqrt{{\mathtt{25}}}}){!}$$=5!=120