Official solution
General term Tr+1 = 60Cr, \[{7^{{{60 - r} \over 5}}}{3^{{r \over {10}}}}\]
\[ \therefore \] for rational term, r = 0, 10, 20, 30, 40, 50, 60
\[ \Rightarrow \] no of rational terms = 7
\[ \therefore \] number of irrational terms = 54