General term of $\left(3^{1 / 5}+7^{1 / 3}\right)^{100}$ is given by
$T_{r+1} ={ }^{100} C_{r}\left(3^{1 / 5}\right)^{100-r}\left(7^{1 / 3}\right)^{r}$
$={ }^{100} C_{r} \cdot 3 \frac{100-r}{5} \cdot 7^{\frac{r}{3}}$
For a rational term, $\frac{100-r}{5}$ and $\frac{I}{3}$ must be integer.
Hence, $r=0,15,30,45,60,75,90$
$\therefore $ There are seven rational terms.
Hence, number of irrational terms
$=101-7=94$