Q13/084) The sum of the rational terms in the expansion of (2^(1/2) +3^(1/5))^10 is

For it the power of 2 and of 3 both should be integer

So the terms should be (10C 2p)  (2^(1/2)^2p * (3^(1/5)^ 5q) where 2p + 5q = 10

Solution of 2p + 5q =1 0 are p = 0 q =2 or q = 0 p = 5

P = 0 q = 2 give (10c0) 3^2 = 9

P = 5 q = 0 give (10c10) 2^5 = 32

So the rational terms are 32 and 9 and sum is 41