sqrt question
04-06-2017, 05:46 PM
Post: #6
 Han Senior Member Posts: 1,882 Joined: Dec 2013
RE: sqrt question
(04-06-2017 04:51 PM)KeithB Wrote:  pier4r:

But we all know that sqrt(36) = sqrt(4*9) = sqrt(4) * sqrt(9), right?

So the reverse is true: sqrt(-4) * sqrt(-9) = sqrt(-4*-9) = sqrt(36). This, of course, is the only way to do it in the real numbers and get an answer.

You are mixing mathematical rules, and you are also ignoring order of operations.

1. $$\sqrt{a}$$ is usually only defined for $$a \ge 0$$. The multiplicative property $$\sqrt{a}\cdot \sqrt{b} = \sqrt{a\cdot b}$$ likewise only applies to non-negative values of $$a$$ and $$b$$. Another way of putting it is that this property is a result of the assumption that the domain of $$\sqrt{x}$$ is the set of non-negative real numbers.

2. The order of operations dictate that exponents are evaluated first. So $$\sqrt{-4} \cdot \sqrt{-9} = -6$$ -- however this assumes that we are not using the $$\sqrt{x}$$ function as described in #1. In fact, we have have implicitly assumed that the $$\sqrt{\quad }$$ operator is defined for negative values, and that the evaluation is $$i\cdot \sqrt{|x|}$$

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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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