Poll

3 votes (7.69%)
16 votes (41.02%)
11 votes (28.2%)
1 vote (2.56%)
2 votes (5.12%)
No votes (0%)
1 vote (2.56%)
3 votes (7.69%)
2 votes (5.12%)
5 votes (12.82%)

39 members have voted

Wizard
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Wizard
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April 26th, 2016 at 5:00:34 PM permalink
Quote: ChesterDog

To make √, I cut and pasted it from Excel.



How did you make it in Excel?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
MathExtremist
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April 26th, 2016 at 5:05:54 PM permalink
Quote: Wizard

How did you make it in Excel?



In my version, Insert -> Symbol -> Subset=Mathematical Operators (or just scroll down until you find it).
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
Wizard
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April 26th, 2016 at 5:17:22 PM permalink
Quote: MathExtremist

In my version, Insert -> Symbol -> Subset=Mathematical Operators (or just scroll down until you find it).



Thanks, in responding to this, I accidentally clicked your post and removed some of it, for which I apologize.

Let's try that: √

In fact, let's try some other symbols while I'm at it: ∫£π≠©≤÷®⅓
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Toes14
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April 26th, 2016 at 5:40:47 PM permalink
the square root of a negative number is i, and is numerically equal to -1. The expression becomes i * i, or -1 * -1, so the answer is 1.
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beachbumbabs
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April 26th, 2016 at 5:47:59 PM permalink
Quote: Toes14

the square root of a negative number is i, and is numerically equal to -1. The expression becomes i * i, or -1 * -1, so the answer is 1.



And with that, we have come full circle to my answer early on. Really interesting journey.
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ChesterDog
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April 26th, 2016 at 5:49:46 PM permalink
Quote: Toes14

the square root of a negative number is i, and is numerically equal to -1. The expression becomes i * i, or -1 * -1, so the answer is 1.



Here's a nice Khan Academy video about the powers of i.
Doc
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April 26th, 2016 at 5:59:52 PM permalink
Quote: Toes14

the square root of a negative number is i, and is numerically equal to -1. The expression becomes i * i, or -1 * -1, so the answer is 1.

Where in the world did that come from? So the square roots of -6, -584, and -275 are all equal to i ?????
Last edited by: Doc on Apr 26, 2016
MrGoldenSun
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April 27th, 2016 at 6:30:13 AM permalink
Quote: Toes14

the square root of a negative number is i, and is numerically equal to -1. The expression becomes i * i, or -1 * -1, so the answer is 1.



No, i is the square root of NEGATIVE ONE. It's not the square root of any negative number.
RS
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April 27th, 2016 at 9:09:30 AM permalink
Quote: Wizard

p.s. How do you make the square root symbol?



Such a n00b, you gotta draw it! Quoted from my post earlier:

Quote: RS

           ____________
\ /
\ /
\ /



Quote: davethebuilder

On your keyboard type 221A then hit Alt and x at the same time.



221A then Alt+X did nothing.

I tried Alt+221A, but all that did was open up gmail....huh?
Wizard
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April 27th, 2016 at 9:27:10 AM permalink
I revise my answer from +/- 6 to -6 only.


sqrt(-4) * sqrt(-9) =
2*sqrt(-1) * 3*sqrt(-1) =
6 * i * i =
6 * -1 =
-6
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
panda1314
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April 27th, 2016 at 9:32:30 AM permalink
Quote: rsactuary

to be more specific, the square root of -1 is defined as i, or similarly defined as i^2 = -1

++1
MathExtremist
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April 27th, 2016 at 9:40:59 AM permalink
Quote: panda1314

++1

Who else read that and thought "that won't compile"?
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
MrGoldenSun
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April 27th, 2016 at 10:22:28 AM permalink
Quote: Wizard

I revise my answer from +/- 6 to -6 only.



Welcome to the winning team.
Wizard
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April 27th, 2016 at 10:37:49 AM permalink
Quote: MathExtremist

Who else read that and thought "that won't compile"?



++; on that sentiment.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
davethebuilder
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April 27th, 2016 at 11:56:17 AM permalink
RS - Use the keypad, not the numbers at the top of the keyboard.
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RS
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April 27th, 2016 at 12:03:08 PM permalink
Quote: davethebuilder

RS - Use the keypad, not the numbers at the top of the keyboard.



My Chromebook doesn't have a keypad!
Romes
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April 27th, 2016 at 1:51:01 PM permalink
Quote: Wizard

...Regarding the topic at hand, when I was in high school I was taught that sqrt(x^2) = +/- x. Were my teachers wrong or has the square root convention changed since the early 1980's?

p.s. How do you make the square root symbol?

This was also my teachings though when going through college and taking upper level math classes I recall something about principal root being mentioned? That's why I took the problem to be positive because you didn't specify a symbol in front of the roots.

I make the root symbol by clicking quote on someone else and copy pasting =P.

I believe on windows you can hold down CTRL or CRTL+Function (windows key) or something and then use the num pad to make ALL KINDS of symbols.

http://symbolcodes.tlt.psu.edu/accents/codealt.html
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davethebuilder
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April 27th, 2016 at 5:15:24 PM permalink
Quote: RS

My Chromebook doesn't have a keypad!



ALT codes require a numeric keypad. Otherwise you should search your Operating System to see if a Character Map or Math Symbol library has been included. If not, you may need to talk to Technical Support.
Casino Enemy No.1
andysif
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April 27th, 2016 at 8:31:21 PM permalink
I think there is no point in using the spoiler anymore

Even if you take only the principal root (the positive one), there is still 2 trains of thoughts

¡Ô(-4) = ¡Ô4 * ¡Ô-1 = 2i . . . 2i * 3i = -6

But while doing
¡Ô(-4) = ¡Ô4 * ¡Ô(-1)
you are essentially also saying that
¡Ô36 = ¡Ô(-4) * ¡Ô(-9)
So 6 should be good as well.

So my vote for both 6 and -6 stands
andysif
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April 27th, 2016 at 8:33:08 PM permalink
Quote: andysif

I think there is no point in using the spoiler anymore

Even if you take only the principal root (the positive one), there is still 2 trains of thoughts

¡Ô(-4) = ¡Ô4 * ¡Ô-1 = 2i . . . 2i * 3i = -6

But while doing
¡Ô(-4) = ¡Ô4 * ¡Ô(-1)
you are essentially also saying that
¡Ô36 = ¡Ô(-4) * ¡Ô(-9)
So 6 should be good as well.

So my vote for both 6 and -6 stands


that funny symbol is supposed to be sqrt
ChesterDog
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April 27th, 2016 at 8:52:03 PM permalink
Quote: andysif

I think there is no point in using the spoiler anymore

Even if you take only the principal root (the positive one), there is still 2 trains of thoughts

√(-4) = √4* √(-1) = 2i . . . 2i * 3i = -6

But while doing
√(-4) = √4* √(-1)
you are essentially also saying that
√36= √(-4) * √(-9)
So 6 should be good as well.

So my vote for both 6 and -6 stands



(I changed the strange symbol in your quote to the radical sign.) Watch the beginning of this Khan Academy video for a warning not to do your step √36= √(-4) * √(-9).
MathExtremist
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April 27th, 2016 at 9:32:57 PM permalink
Quote: ChesterDog

a warning not to do your step √36= √(-4) * √(-9).

Here's why:
Given
a) i = √-1
b) i * i = -1
c) √1 = 1
d) 1 = -1 * -1
Suppose √1 = √-1 * √-1. Then:
1) 1 = √-1 * √-1
2) 1 = i * i
3) 1 = -1
Uhh...
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
OnceDear
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April 28th, 2016 at 6:20:18 AM permalink
Quote: MathExtremist


Quote:

a warning not to do your step √36= √(-4) * √(-9).



Here's why:
Given
a) i = √-1
b) i * i = -1
c) √1 = 1
d) 1 = -1 * -1
Suppose √1 = √-1 * √-1. Then:
1) 1 = √-1 * √-1
2) 1 = i * i
3) 1 = -1
Uhh...



Or even more simply. Rules of precedence say that step is invalid. Exponentiation has to precede multiplication. BEDMAS ( or BODMAS)
$:o)
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RS
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April 28th, 2016 at 6:21:34 AM permalink
Quote: MathExtremist

Here's why:
Given
a) i = √-1
b) i * i = -1
c) √1 = 1
d) 1 = -1 * -1
Suppose √1 = √-1 * √-1. Then:
1) 1 = √-1 * √-1
2) 1 = i * i
3) 1 = -1
Uhh...



Proof by contradiction! I like it.
Wizard
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April 28th, 2016 at 6:40:24 AM permalink
Quote: andysif

But while doing
¡Ô(-4) = ¡Ô4 * ¡Ô(-1)
you are essentially also saying that
¡Ô36 = ¡Ô(-4) * ¡Ô(-9)
So 6 should be good as well.



Agreed, we can stop using spoiler tags.

I think your argument there violates the order of operations. You have to evaluate the square root first.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
TwoFeathersATL
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April 28th, 2016 at 7:42:58 AM permalink
Quote: Wizard

Agreed, we can stop using spoiler tags.

I think your argument there violates the order of operations. You have to evaluate the square root first.


Heaven forbid anyone should break any of the rules.
The world is flat, and you had better agree....
Youuuuuu MIGHT be a 'rascal' if.......(nevermind ;-)...2F
Romes
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April 28th, 2016 at 8:49:21 AM permalink
Quote: TwoFeathersATL

Heaven forbid anyone should break any of the rules.
The world is flat, and you had better agree....

2F... <3

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MathExtremist
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April 28th, 2016 at 9:06:41 AM permalink
Quote: OnceDear

Or even more simply. Rules of precedence say that step is invalid. Exponentiation has to precede multiplication. BEDMAS ( or BODMAS)
$:o)

I learned PEMDAS, but I'm on the Las Vegas side of the pond. However, the general form
(A*B)^N = A^N * B^N
holds under many scenarios, including when N is an integer and when at least one of A and B are non-negative. But it's a mistake to assume that it always holds.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
TheGrimReaper13
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April 28th, 2016 at 9:19:52 AM permalink
Quote: TwoFeathersATL

Heaven forbid anyone should break any of the rules.
The world is flat, and you had better agree....

Heaven forbid we ever get out of the grade/high school math curriculum. Oh, gambling math. (Speaking of missing posters, at least teliot's errors and gambling musings were half interesting.)
So much bullshit; so little time!
Ibeatyouraces
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April 28th, 2016 at 9:25:06 AM permalink
Quote: TheGrimReaper13

Heaven forbid we ever get out of the grade/high school math curriculum. Oh, gambling math. (Speaking of missing posters, at least teliot's errors and gambling musings were half interesting.)


He's too busy teaching casinos how to train their dealers.
DUHHIIIIIIIII HEARD THAT!
AceTwo
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May 9th, 2016 at 2:08:53 PM permalink
sqrt(a)*sqrt(b)=sqrt(a.b)
Taking this formula which applies to complex number the equation becomes sqrt(36) = 6 if we use this principal square root terminology.
Wheras as other calculated you get -6 for the principal square root if you do each square root separetely.
So the bottom line is you cannot talk about principal square roots when dealing with complex numbers.
The answer is +-6.
TheGrimReaper13
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May 9th, 2016 at 2:13:02 PM permalink
The roots of negative numbers DO NOT involve principal square roots.

In any event, the question was not stated in the form of any standard equation. To me, "?" means possibilities; and "x" means conventional usage.
So much bullshit; so little time!
MathExtremist
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May 9th, 2016 at 7:46:03 PM permalink
Quote: AceTwo

sqrt(a)*sqrt(b)=sqrt(a.b)

Not when both a and b are negative. See the prior page.
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
gary55
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May 9th, 2016 at 8:51:23 PM permalink
is there a point to this question ? and do we get the right answer eventually
TheGrimReaper13
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May 9th, 2016 at 10:25:24 PM permalink
Quote: gary55

is there a point to this question ? and do we get the right answer eventually

The only point to be made here is that high school students are taught to instinctively replace the roots of negative numbers - particularly the square roots - with imaginary numbers written in terms of i, before proceeding with their further calculations. It just becomes second nature, and with other math steps and conventions, the more math you learn and practise. At some point, you are taught also the WHY of it all.
So much bullshit; so little time!
gary55
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May 10th, 2016 at 4:13:19 AM permalink
just for the record i voted -i 6
shallnot
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September 29th, 2016 at 1:02:52 AM permalink
An expanded version of Wizard's revision to "-6 only" that avoids the whole "but the square root of x is +/- y" diversion:

sqrt(-4) * sqrt(-9) =
sqrt(-1) * sqrt(4) * sqrt(-1) * sqrt(9) =
i * sqrt(4) * i * sqrt(9) =
i^2 * sqrt(4 * 9) =
i^2 * sqrt(36) =
-1 * sqrt(36) =

do a factor tree on 36 to get:

-1 * sqrt(2 * 2 * 3 * 3) =

bring the 2 and 3 out in pairs:

-1 * 2 * 3 =
-6
Last edited by: shallnot on Sep 29, 2016
beachbumbabs
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September 29th, 2016 at 6:44:19 AM permalink
Quote: shallnot

An expanded version of Wizard's revision to "-6 only" that avoids the whole "but the square root of x is +/- y" diversion:

sqrt(-4) * sqrt(-9) =
sqrt(-1) * sqrt(4) * sqrt(-1) * sqrt(9) =
i * sqrt(4) * i * sqrt(9)
i^2 * sqrt(4 * 9)
i^2 * sqrt(36)
-1 * sqrt(36)

do a factor tree on 36 to get:

-1 * sqrt(2 * 2 * 3 * 3)

bring the 2 and 3 out in pairs:

-1 * 2 * 3 =
-6



Hi, shallnot, and welcome to the forum! Thanks for the proof.
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