If n is the number of irrational terms in the expansion of ${(3^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}+5^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$8$}\right.})}^{60},$ then $(n–1)$ is divisible by: 

${(3^{1/4}+5^{1/8})}^{60}$

${ }^{60}{C}_r{3}^{\frac{60-r}{4}}{.5}^{r/8}$

For rational terms, $r =0,8,16, 24, \dots \dots .. 56$  i.e. 8 terms

Irrational terms, $61–8=53=n$

$n–1=52$