Hi. I'm in the initial review section of a pre-calc book and a little confused about something. The problem is to rationalize the denominator of the following expression:

The answer the book gives is

However, when I work through the problem I end up with:

Because of the properties of nth Roots (given in the book) which indicate that

but

Have I missed something, or did the book make a mistake? I suppose it is a small point, but I keep getting confused about the issue of roots and absolute values.