(2^1/2 + 3^1/5 )¹⁰

a =2^1/2 _, b = 3^1/5

 

t_r+1 = nC_r a^(n-r) b^r

 

for r = 0 we get 2^1/2 power 10 and the other term power 0 which is rational

 

now for further r values for the term to b rational

it shud be a multiple of 5 since we have 3^1/5

so we take r = 5

but r = 5 means first term is (2)⁵ which is irrational

 

so now r =10

i think there r the only two terms

hence sum =

(2)¹⁰ + 3^{1/5 * 10}

= 32 + 9 = 41

But pls correct me if wrong