The number of integral terms in expansion $(\sqrt [2]{3} + \sqrt [ 8 ]{ 5 } )^{256}$ is

General term,

$\begin{array}{l} \mathrm{T}_{\mathrm{r}+1}={ }^{256} \mathrm{C}_{\mathrm{r}}(\sqrt{3})^{256-r}\left({ }^{8} \overline{5}\right)^{\mathrm{r}} \\ ={ }^{256} \mathrm{C}_{\mathrm{r}}(3)^{(256-r) / 2}(5)^{r / 8} \end{array}$

Now this term is an integer if $\frac{256-r}{2}, \frac{r}{8}$ will be an integer, for which

$r=0,8,16, \ldots, 256$

For A.P., $0,8,16,24, \ldots, 256$ number of terms will be

$=\frac{256}{8}+1=33$

Hence, there are 33 integral terms.