Question

The sum of the rational terms in the expansion of

$\left( \sqrt{2} + 3^{1/5} \right)^{10}$ is

• A. 46
• B. 42
• C. 41
• D. None of these

Answer 1

Answer: (C)

41

Answer 2

The given expansion $\left( \sqrt{2} + 3^{1/5} \right)^{10}$ =

$\sum_{r = 0}^{10}{10C_{2}2^{\frac{10 - r}{2}}3^{r/5}}$.

The rational terms correspond to r = 0, r = 10. Hence the sum of rational terms = ¹⁰C₀ 2⁵ + ¹⁰C₁₀ 3² = 32 + 9 = 41.