TITLE: Denoting all the cube roots of a real number
QUESTION [9 upvotes]: This may be a very simple question to ask, but I am confused with these definitions and would like to clarify here.
$\sqrt{81} = 9$. But $\sqrt{81} \ne -9$ because $\sqrt{}$ is used to represent the principal root. 
So, If I want to represent both the roots, I have to mention it as $\pm\sqrt{81} = \pm 9$.
We know every real number ($\ne 0$) has three cube roots, one real and two complex. So, if we say $\root 3 \of {27}$, it means the principal cube root, which is $3$.
If so, 

(a) How do we indicate that we are referring to all the three cube roots
  together (like $\pm \sqrt{81}$ for square roots) 
  because $\root 3 \of {}$ refers to only principal cube root?
(b) Why are there no commonly accepted guidelines to decide the principal
  cube root because in some places, it is the real number while some
  books refer it to the one in positive imaginary axis.

Please help me to clear my doubts.

REPLY [2 votes]: When using the cubic formula (like the quadratic formula, except for cubics), the first root is found using the principal cube root, and in this case it is the one with the LARGES REAL PART, if it is a tie, you chose the one with the larges imaginary that is in the tie. The second root is the one with the largest imaginary part that is not the principle cube root. The third is the other. If you do not do this, you will not get the right answer in the cubic formula.