Question

Find the number of integral terms in the expansion of $(\sqrt{3}+\sqrt[8]{85}{)}^{256}$

• A. $33$
• B. $34$
• C. $35$
• D. $32$

Answer 1

The correct option is A $33$

$(3^{1/2}+5^{1/8}{)}^{256}$

$T_{r+1}{=}^{256}{C}_r(\sqrt{3}{)}^{256-r}{5}^{\frac{r}{8}}$

For integral terms $\frac{256-r}{2},\frac{r}{8}$ are both positive integer

$\therefore r=0,8,16,....256$

$256=0+(n-1)8$ using $t_n=a+(n-1)d$

$\frac{256}{8}=n-1$

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

$n$$=32+1=33$