Question

Sum of all the rational terms in the expansion of ${(2^{1/3}+3^{1/2})}^6$ is

• A. $31$
• B. $83$
• C. $27$
• D. $91$

Answer 1

Answer: (A)

$31$

$(2^{1/3}+3^{1/2}{)}^6$

$2^{6/3}$ and $3^{6/2}$ are the only rational terms possible

$2^{6/3}\times 3^o=2^{6/3}=2^2=4$

$3^{6/2}\times 2^o=3^{6/2}=3^3=27$

The other terms when expanded atleast one of the two terms will be irrational. Hence the sum of rational terms $=4+27$

$=31$.