Question

The sum of the rational terms in the expansion of ${(\sqrt{2}+\sqrt[5]{53})}^{10}$ is

• A. $32$
• B. $9$
• C. $41$
• D. none of these

Answer 1

The correct option is C $41$

$T_{r+1}={}^{10}{C}_r{2}^{5-\frac{r}{2}}{3}^{\frac{r}{5}}$
Hence we get two rational terms, $T_1$ and $T_{11}$
$T_1={}^{10}{C}_0{2}^5$$=32$
$T_{11}={}^{10}{C}_{10}{3}^2$ $=9$
$T_1+T_{11}=32+9$
$=41$