The sum of the rational term in the binomial expansion of $\left(\sqrt{2}+3^{1 / 5}\right)^{10}$ is

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Aicharya · Accepted Answer

Rational terms are $T_{11}, T_1$ $\begin{aligned} & \mathrm{T}_{11}={ }^{10} \mathrm{C}_{10}\left(3^{1 / 5}\right)^{10}(\sqrt{2})^0=9 \\ & \mathrm{~T}_1={ }^{10} \mathrm{C}_0\left(3^{\frac{1}{5}}\right)^0 \cdot(\sqrt{2})^{10}=32 \end{aligned}$
Sum of rational terms $=41$

The sum of the rational term in the binomial expansion of $\left(\sqrt{2}+3^{1 / 5}\right)^{10}$ is

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