Which terms are rational in the expansion of (\sqrt{3} + \frac{1}{\sqrt[4]{6}})^{15} . list the rational terms and justify why the others are not rational.

Binomial expansion formula,

Where,

∵ both and are irrational numbers,

And, if the power of √3 is even, it converted to a rational number,

If its power is odd it remained as irrational number,

But, the product of a rational number and irrational number is irrational,

Thus, all terms in the above expansion are irrational. ( which can not expressed in the form of p/q, where, p and q are integers s.t. q ≠ 0 )

answer:

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