Thread: Properties of Roots and Absolute Values

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.

You can usually determine the correct answer by comparing when (for instance) y = -2 and y = 2.
If y = -2, then the fourth root (of -8) is imaginary. So there must be an assumption that y is positive in this example.