> THEOREM: Let p,q be rational numbers. Then sqrt(p +/- sqrt(q)) > can be expressed as sqrt(a) +/- sqrt(b) for some > rational numbers a,b if and only if p > 0 and p^2 - q > is a perfect square.
This should begin with "Let p,q be nonzero rational numbers such that sqrt(q) is irrational". Chrystal doesn't say this in his statement of the result, but these assumptions probably appear a few pages earlier. Note to anyone writing a book or planning to write a book: To increase the value of your book as a reference, key results should be stated as much as possible in a way that is "locally correct" and "locally understandable".