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$T h e n u m b e r o f i n t e g r a l t e r m s i n t h e e x p a n s i o n o f {(\sqrt{3} + \sqrt[8]{5})}^{256} i s$

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a

32

b

33

c

34

d

35

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detailed solution

Correct option is B

General term of the binomial expansion 3+58256is Tr+1=C256,r3256−r58r=C256,r3128−r25r8Terms are integers, then the value of r such that it is multiple of 8 and less than or equal to 256 Hence, the possible values of r are 0,8,16,...256. The number of value of r is 33. hence the number of rational terms is 33.

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