If n is the number of irrational terms in the expansion of  ${\left(3^{\frac{1}{4}}+5^{\frac{1}{8}}\right)}^{60}$, then $(n-1)$ is divisible by 

 ${\left(3^{\frac{1}{4}}+5^{\frac{1}{8}}\right)}^{60}$

$T_{r+1}{=}^{60}{C}_r{\left(3\right)}^{\frac{60-r}{4}}{.5}^{\frac{r}{8}}$ 

For rational terms r = 0, 8, 16, 
24,32,40,48,54.
i.e. 8 terms
n = irrational terms = 61-8 =53
n – 1 = 53-1 = 52