Official solution
General term of the expression,
\[{T_{r + 1}} = {}^n{C_r}{\left( {{3^{{1 \over 2}}}} \right)^{n - r}}{\left( {{5^{{1 \over 8}}}} \right)^r}\]
\[ = {}^n{C_r}{\left( 3 \right)^{{{n - r} \over 2}}}{\left( 5 \right)^{{r \over 8}}}\]
We will get integral term when \[{{n - r} \over 2}\] and \[{r \over 8}\] are integer
\[ \therefore \] (1) n - r is multiple of 2
\[ \Rightarrow \] n - r = 0, 2, 4, ......
(2) r is multiple of 8
\[ \Rightarrow \] r = 0, 8, 16, .......
From this two conditions common values are = 0, 8, 16, ....... which will becomes integral terms.
Given that there are 33 integral terms.
Here first integral term at 0th position.
Second integral term at 8th position.
\[ \therefore \] 33th integral term will be at = 0 + (33 - 1)8 = 256
So, there should be at least 256 terms.