Binomial Theorem
Rational and Irrational Terms
Premium Question
Grade 11
Question:
The number of irrational terms in the expansion of $(\sqrt[3]{2} + \sqrt[4]{3})^{12}$ is:
(1) $13$
(2) $11$
(3) $2$
(4) $9$
Step-by-Step Solution
Key Concept: First find how many of the 13 terms $T_{r+1} = \binom{12}{r} 2^{(12-r)/3} 3^{r/4}$ are rational (i.e. both exponents are integers), and then subtract this count from the total number of terms.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)