Indices question

Why is it that when we normally square root a number the answer must have a +-, e.g. sqrt(9) = +-3, but that when there is a fractional index, the positive root is taken when square rooting, e.g. sqrt(9^3/2) = 3^3 = 27 and not +-3^3 = +-27. Sorry I'm just confused about it- thanks for any help

You don't take the negative square root. It would b wrong to say that $\surd 4 = 2$. So $\surd 4 = 4^{1/2}=2 \neq -2$.
If $x^2= 4$ then sure, $x=\pm 2$ but it is important to realise that you are not just simply taking the square root of both sides.
This is a misconception many people have so please feel free to ask any more questions regarding the square root of you are confused about anything.

Sorry but I still don't understand, if the square root of 4 is +-2 then why would you sometimes take the negative value and sometimes not, and how do you know if you should?