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  • The number of integral terms in the expansion of <img alt="(\sqrt{3}+\sqrt[8]{5})^{256}" src="https://entrancecorner.oncodecogs.com/gif.latex?%28%5Csqrt%7B3%7D&plus;%5Csqrt%5B8%5D%7B5%7D%29%5E%

The number of integral terms in the expansion of (\sqrt{3}+\sqrt[8]{5})^{256} is 

Option: 1

32


Option: 2

33


Option: 3

34


Option: 4

35


Answers (1)

best_answer

T_{r+1}={ }^{256} C_r(\sqrt{3})^{256-r}(\sqrt[8]{5})^r={ }^{256} C_r(3)^{\frac{256-r}{2}}(5)^{r / 8}

Terms would be integral if  and  both are positive integer.

As 0 \leq r \leq 256, \quad \therefore r=0,8,16,24, \ldots . ., 256

For above values of r, \left(\frac{256-r}{2}\right)   is also an integer. 

∴ Total number of values of r = 33.
 

Posted by

Anam Khan

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