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The rational term in the expansion of (\sqrt[3]{3}+\sqrt{2})^5 is

Option: 1

60


Option: 2

61


Option: 3

62


Option: 4

59


Answers (1)

The rth term is { }^5 C_r\left(3^{1 / 3}\right)^r\left(2^{1 / 2}\right)^{5-t}

For rational term r is a multiple of 3 i.e.

r = 3m and 5 - 3m is a multiple of 2

Also 5 - 3m >0 Hence m =1

\Rightarrow \mathrm{r}=3 \Rightarrow \text { rational term }={ }^3 \mathrm{C}_3(3)(2)

= 60 

Posted by

Sumit Saini

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