Question

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

• A. $32$
• B. $25$
• C. $41$
• D. $9$

Answer 1

The correct option is C $41$

$T_{r+1}{=}^{10}{C}_r(2{)}^{\frac{r}{2}}\cdot {\left(3^{\frac{1}{5}}\right)}^{10-r}{=}^{10}{C}_r\cdot 2^{\frac{r}{2}}\cdot 3^{\frac{10-r}{5}};r=0,1,2,$..,$9,10$

$\therefore$ For rational terms, $r=0,r=10$

So, sum of rational terms $=9+32=41$.