What is the number of rational terms in the expansion of (3^(1/2) + 5^(1/4))^12?
A.2
B.3
C.4✓ Correct
D.6
Explanation
General term: T_(r+1) = C(12,r) · 3^((12-r)/2) · 5^(r/4). For rational, (12-r)/2 must be integer (so 12-r even, r even) AND r/4 must be integer (so r divisible by 4). So r ∈ {0, 4, 8, 12}, giving 4 rational terms.
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