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Topic: simplify radicals
Replies: 24   Last Post: Jan 8, 2007 9:09 PM

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Dave L. Renfro

Posts: 4,792
Registered: 12/3/04
Re: simplify radicals - regular 12-gon
Posted: Dec 22, 2006 1:05 PM
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Dave L. Renfro wrote (in part):

> 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".

Dave L. Renfro

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