Imagine this math problem
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39 members have voted
Quote: ChesterDogTo make √, I cut and pasted it from Excel.
How did you make it in Excel?
Quote: WizardHow did you make it in Excel?
In my version, Insert -> Symbol -> Subset=Mathematical Operators (or just scroll down until you find it).
Quote: MathExtremistIn 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
Quote: Toes14the 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.
Where in the world did that come from? So the square roots of -6, -584, and -275 are all equal to i ?????Quote: Toes14the 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.
Quote: Toes14the 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.
Quote: Wizardp.s. How do you make the square root symbol?
Such a n00b, you gotta draw it! Quoted from my post earlier:
Quote: RS____________
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Quote: davethebuilderOn 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?
sqrt(-4) * sqrt(-9) =
2*sqrt(-1) * 3*sqrt(-1) =
6 * i * i =
6 * -1 =
-6
++1Quote: rsactuaryto be more specific, the square root of -1 is defined as i, or similarly defined as i^2 = -1
Who else read that and thought "that won't compile"?Quote: panda1314++1
Quote: WizardI revise my answer from +/- 6 to -6 only.
Welcome to the winning team.
Quote: MathExtremistWho else read that and thought "that won't compile"?
++; on that sentiment.
Quote: davethebuilderRS - Use the keypad, not the numbers at the top of the keyboard.
My Chromebook doesn't have a keypad!
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.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?
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
Quote: RSMy 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.
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
Quote: andysifI 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
Quote: andysifI 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).
Here's why:Quote: ChesterDoga warning not to do your step √36= √(-4) * √(-9).
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...
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)
Quote: MathExtremistHere'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.
Quote: andysifBut 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.
Quote: WizardAgreed, 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....
2F... <3Quote: TwoFeathersATLHeaven forbid anyone should break any of the rules.
The world is flat, and you had better agree....
I learned PEMDAS, but I'm on the Las Vegas side of the pond. However, the general formQuote: OnceDearOr even more simply. Rules of precedence say that step is invalid. Exponentiation has to precede multiplication. BEDMAS ( or BODMAS)
$:o)
(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.
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.)Quote: TwoFeathersATLHeaven forbid anyone should break any of the rules.
The world is flat, and you had better agree....
Quote: TheGrimReaper13Heaven 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.
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.
In any event, the question was not stated in the form of any standard equation. To me, "?" means possibilities; and "x" means conventional usage.
Not when both a and b are negative. See the prior page.Quote: AceTwosqrt(a)*sqrt(b)=sqrt(a.b)
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.Quote: gary55is there a point to this question ? and do we get the right answer eventually
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
Quote: shallnotAn 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.
