Question

The sum of rational terms in $(\sqrt{2} + \sqrt[3]{3} + \sqrt[6]{5})^{10}$ is

• A. 12632
• B. 1260
• C. 126
• D. 1262

Answer 1

Answer: (A)

12632

Answer 2

General term = $\frac{10!}{\alpha!\beta!\gamma!}$ 2^a/2 3^b/3 5^g/6

a = 0, 2, 4, 6,8, 10

b = 0, 3, 6 g = 0, 6

Hence possible sets = (4, 6, 0), (4, 0, 6), (10, 0, 0)

Hence there are 3 rational terms

Sum =$\frac{10!}{4!6!}$ 2² 3² + $\frac{10!}{4!6!}$ 2² 5 +$\frac{10!}{10!}$ 2⁵ = 12632