In the expansion of 71/3+111/96561,

General term is  6561Cr76561−r311r9.To make the term free of radical sign, r should be a multiple of 9. ∴ r=0,9,18,27,…,6561.Hence, there are 730 rational terms. The greatest binomial coefficients are 6561C6561−12 and 6561C6561+12 or 6561C3280 and 6561C3281.Now, 3280 are 3281 are not a multiple of 3; hence, both terms involving greatest binomial coefficients are irrational.