Question

How do you simplify `6root4 9 +2 root3 9 +2 root4 9 - 3 root3 9`?

Answer 1

`sqrt3(+-6+-2)-9^(1/3)` = `sqrt3(+-6+-2)-2.08)`, nearly.
The four values are `11.78, 4.85, -9.01 and -15.94`, nearly.

Explanation:

`9^(1/4)=(9^(1/2))^(1/2)=(+3)^(1/2)=+-sqrt3`.

The first and third tems add up to `sqrt3(+-6+-2)`.

The second and fourth add up to `-9^(1/3`..

So, the expression simplifies to `sqrt3(+-6+-2)-9^(1/3)`.
There is only one real value 2.08, nearly, for #9^(1/3).

In general, `a^(1/n)` has n values. The complex values occur in conjugate pairs. For example, the values `1^(1/3)`are `1, +-i`.,