sqrt question
04-06-2017, 06:18 PM (This post was last modified: 04-06-2017 06:21 PM by Han.)
Post: #8
 Han Senior Member Posts: 1,883 Joined: Dec 2013
RE: sqrt question
(04-06-2017 06:03 PM)KeithB Wrote:  So to summarize, by assuming sqrt(-4) is a valid operation we are automatically going to interpret it as 2i.

No, the point was that in choosing to evaluate $$\sqrt{-4} \cdot \sqrt{-9}$$ to be equal to -6 (by following the order of operations), we have implicitly made the assumption that $$\sqrt{ x } = i \sqrt{|x|}$$ for $$x < 0$$.

The conventional use of $$\sqrt{x}$$ is that it is the positive square root of $$x$$. There is no single convention, however, for $$\sqrt{x}$$ if $$x < 0$$.

EDIT: One could also argue that we may have actually implicitly assumed that $$\sqrt{x} = -i \sqrt{|x|}$$ for $$x < 0$$. We still get -6, but all the more reason that there is no single convention for $$\sqrt{x}$$ for negative values of $$x$$.

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 Messages In This Thread sqrt question - KeithB - 04-06-2017, 03:25 PM RE: sqrt question - pier4r - 04-06-2017, 04:01 PM RE: sqrt question - Namir - 04-06-2017, 04:02 PM RE: sqrt question - KeithB - 04-06-2017, 04:51 PM RE: sqrt question - Han - 04-06-2017, 05:46 PM RE: sqrt question - pier4r - 04-06-2017, 05:15 PM RE: sqrt question - KeithB - 04-06-2017, 06:03 PM RE: sqrt question - Han - 04-06-2017 06:18 PM RE: sqrt question - Claudio L. - 04-07-2017, 01:23 PM RE: sqrt question - Han - 04-07-2017, 04:48 PM RE: sqrt question - Claudio L. - 04-07-2017, 09:15 PM RE: sqrt question - Han - 04-07-2017, 10:54 PM RE: sqrt question - Claudio L. - 04-09-2017, 03:59 AM RE: sqrt question - David Hayden - 04-24-2017, 09:36 PM RE: sqrt question - Claudio L. - 04-26-2017, 03:08 AM RE: sqrt question - Han - 04-28-2017, 06:09 PM RE: sqrt question - nsg - 04-07-2017, 11:34 PM RE: sqrt question - Vtile - 04-09-2017, 10:41 AM RE: sqrt question - nsg - 04-09-2017, 05:26 PM RE: sqrt question - Vtile - 04-09-2017, 11:07 PM RE: sqrt question - nsg - 04-10-2017, 01:44 AM RE: sqrt question - Vtile - 04-25-2017, 11:38 PM

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