The number of irrational terms in the expansion of `(4^(1/5)+7^(1/10))^45` is

Explanation

The general term `T_{r+1}` in the given expansion is given by

`\ ^{45} C_{r}(4^{1 / 5}\)^{45-r}(7^{1 / 10}\)^{r}`

For `T_{r+1}` to be an integer, we must have `\frac{r}{5}` and `\frac{r}{10}` as integers `\{i}, \{e} .0 \leq r \leq 45`

`\therefore r=0,10,20,30` and 40

Hence, there are 5 rational and `41, i`, e., `46-5`, irrational terms.