What is -2 squared?
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 | 19 votes (86.36%) | ||
| | 2 votes (9.09%) | ||
| | 1 vote (4.54%) |
22 members have voted
October 25th, 2017 at 2:51:42 PM
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So, my little cousin was talking about his algebra class the other day, and he told me a question that the teacher asked: "What is negative 2 squared?" He gave the answer the teacher was looking for, which was -4. My cousin explained that order of operations stipulate that the exponent is resolved before the negative is applied. I.e., -22 = -4, but (-2)2 = 4.
I argued (as I learned in school) that the negative (or positive) sign is a property of the number, not an operation, and therefore the answer should be 4. Then I asked him what his calculator (TI-30XS) would say, and sure enough, the calculator gave the answer: -4.
So, I pulled out my trusty HP 48GX from my college days, asked it the same question, and voila! 4. BTW, my Excel 2007 thinks the answer is 4 as well.
Have the rules of math really changed since I was in school? Has the "official" evaluation of -22 changed from 4 to -4 over the past 25 years? Or was I (not to mention my teachers, and my calculator) just wrong all these years?
I argued (as I learned in school) that the negative (or positive) sign is a property of the number, not an operation, and therefore the answer should be 4. Then I asked him what his calculator (TI-30XS) would say, and sure enough, the calculator gave the answer: -4.
So, I pulled out my trusty HP 48GX from my college days, asked it the same question, and voila! 4. BTW, my Excel 2007 thinks the answer is 4 as well.
Have the rules of math really changed since I was in school? Has the "official" evaluation of -22 changed from 4 to -4 over the past 25 years? Or was I (not to mention my teachers, and my calculator) just wrong all these years?
"Dealer has 'rock'... Pay 'paper!'"
October 25th, 2017 at 2:54:46 PM
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I would have said 4 as well. But that hardly ever comes up at work these days.
There's emptiness behind their eyes
There's dust in all their hearts
They just want to steal us all and take us all apart
October 25th, 2017 at 3:00:17 PM
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The iPhone Calculator app agrees with me: 4
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October 25th, 2017 at 3:05:00 PM
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Well, going the opposite way, the square root of -4 doesn't exist.
DUHHIIIIIIIII HEARD THAT!
October 25th, 2017 at 3:19:03 PM
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Now this goes way way back, but wouldn't that be 2i ?Quote: IbeatyouracesWell, going the opposite way, the square root of -4 doesn't exist.
There's emptiness behind their eyes
There's dust in all their hearts
They just want to steal us all and take us all apart
October 25th, 2017 at 3:24:20 PM
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It's positive 4.
A negative times a negative is a positive. That teacher was wrong.
A negative times a negative is a positive. That teacher was wrong.
October 25th, 2017 at 3:25:18 PM
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erm. yes it does. 2j or -2jQuote: IbeatyouracesWell, going the opposite way, the square root of -4 doesn't exist.
the calc that said it's -4 was wrong unless the question was what is -2^2
hmmf. textually it was "What is negative 2 squared?" order of ops is do the squaring, then do the negation.
Psalm 25:16
Turn to me and be gracious to me, for I am lonely and afflicted.
Proverbs 18:2
A fool finds no satisfaction in trying to understand, for he would rather express his own opinion.
October 25th, 2017 at 4:06:18 PM
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I'd say "negative two squared" is four. If you want the answer to be negative four, then ask "what is the negative of two squared?"
Ultimately, it comes down to: What is being squared? Two or negative two?
Better yet, do what I do, and always use parenthesis when something isn't obvious, to show order of operations.
Ultimately, it comes down to: What is being squared? Two or negative two?
Better yet, do what I do, and always use parenthesis when something isn't obvious, to show order of operations.
October 25th, 2017 at 4:11:46 PM
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Quote: JohnnyQNow this goes way way back, but wouldn't that be 2i ?
Imaginary numbers don't exist. Just like the Boogey Man or god.
DUHHIIIIIIIII HEARD THAT!
October 25th, 2017 at 7:09:22 PM
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Numbers don't exist either.
October 25th, 2017 at 7:14:11 PM
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Oh and I am in the +4 camp.
To the third power, it is -8
To the third power, it is -8
October 25th, 2017 at 7:14:39 PM
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Google and Wolfram Alpha both say -2^2 = -4 but (-2)^=4
October 25th, 2017 at 7:27:29 PM
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A negative sign implies multiplication by -1. Exponents come before multiplication in the order of operations.
negative two squared is -4.
(negative 2) squared is 4.
negative two squared is -4.
(negative 2) squared is 4.
October 25th, 2017 at 7:31:53 PM
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My phone gives this answer:
DUHHIIIIIIIII HEARD THAT!
October 25th, 2017 at 7:44:28 PM
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i think the answer is 4
October 25th, 2017 at 7:45:01 PM
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Wikipedia says that it’s ambiguous without parentheses. https://en.m.wikipedia.org/wiki/Order_of_operations#Exceptions
There’s no official precedent for urnary operators.
So I’d assume whether you evaluate it as (-2)(-2) or -(2^2) depends on your software/course/textbook/professor/employer.
Edit: re-read that and it does say that 0 − (2^2) = − 4 is the “correct” way for written maths.
There’s no official precedent for urnary operators.
So I’d assume whether you evaluate it as (-2)(-2) or -(2^2) depends on your software/course/textbook/professor/employer.
Edit: re-read that and it does say that 0 − (2^2) = − 4 is the “correct” way for written maths.
Last edited by: gamerfreak on Oct 25, 2017
October 25th, 2017 at 7:59:46 PM
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While a negative number can be represented by negative one times a positive number, I do not believe it is the definition of a negative number.
If it was, then what is -1?
The answer is of course that -1 is a negative number, and negative numbers are their own things which don't have an implied operation embedded within them.
If it was, then what is -1?
The answer is of course that -1 is a negative number, and negative numbers are their own things which don't have an implied operation embedded within them.
October 25th, 2017 at 8:02:48 PM
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This is very similar to how the square root symbol only resolves the positive root of a number.
October 25th, 2017 at 8:17:18 PM
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Quote: Dalex64While a negative number can be represented by negative one times a positive number, I do not believe it is the definition of a negative number.
If it was, then what is -1?
The answer is of course that -1 is a negative number, and negative numbers are their own things which don't have an implied operation embedded within them.
I think it still needs to be defined. Real numbers include negative numbers. However with Natural numbers, -1 is the additive inverse of 1, where - is an operator, not part of the number itself.
I think I remember getting math problems in school, specifically on the SAT, that specified the numbers in the problem as real or natural.
October 25th, 2017 at 8:17:56 PM
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This screams of a teacher trying to be cute. As noted above, it's ambiguous without the parentheses. If adding an exponent to a negative number, I would input it into computing means with parentheses 100% of the time.
I guess my final answer is that it's a bad question. If asked orally, the answer is +4 without any question. If written on the board and given an equals sign after it, like -2^2=? - that's just a bad question. It would be like giving three equations for four variables, you just tell the person asking the question to provide more information. If on a test, I would have said +/- 4 and explain each with a sentence. However, if a gun was pointed at my head, I think I would go with -4. But still, it's a bad question.
I guess my final answer is that it's a bad question. If asked orally, the answer is +4 without any question. If written on the board and given an equals sign after it, like -2^2=? - that's just a bad question. It would be like giving three equations for four variables, you just tell the person asking the question to provide more information. If on a test, I would have said +/- 4 and explain each with a sentence. However, if a gun was pointed at my head, I think I would go with -4. But still, it's a bad question.
Its - Possessive; It's - "It is" / "It has"; There - Location; Their - Possessive; They're - "They are"
October 26th, 2017 at 2:50:38 AM
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imaginary numbers exist to the same extent as real numbers and irrational numbers. Dunno about the boogeyman man, but agree on the god bit.Quote: IbeatyouracesImaginary numbers don't exist. Just like the Boogey Man or god.
Psalm 25:16
Turn to me and be gracious to me, for I am lonely and afflicted.
Proverbs 18:2
A fool finds no satisfaction in trying to understand, for he would rather express his own opinion.
October 26th, 2017 at 5:14:55 AM
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Thanks for the responses, guys!
I guess what still gets me is that my ~1995 calculator says the answer is 4, and his ~2017 calculator says it's -4. Has conventional thinking shifted on this point over the years?
LOL! Yes, we both agreed that this was a purely academic argument. In real world applications, it will be abundantly clear which answer makes sense.Quote: JohnnyQI would have said 4 as well. But that hardly ever comes up at work these days.
I thought the same thing. Until his calculator stated the opposite.Quote: TigerWuIt's positive 4.
A negative times a negative is a positive. That teacher was wrong.
I would agree with both of these statements!Quote: ahiromuThis screams of a teacher trying to be cute.
...
I guess my final answer is that it's a bad question.
I guess what still gets me is that my ~1995 calculator says the answer is 4, and his ~2017 calculator says it's -4. Has conventional thinking shifted on this point over the years?
"Dealer has 'rock'... Pay 'paper!'"
October 26th, 2017 at 5:21:51 AM
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I think the lesson here is about clarity in writing.
October 26th, 2017 at 8:54:22 AM
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Quote: JoemanI guess what still gets me is that my ~1995 calculator says the answer is 4, and his ~2017 calculator says it's -4. Has conventional thinking shifted on this point over the years?
My guess:
Your 1995 calculator is probably a one line basic calculator (accounting calculator) and his 2017 calculator is a graphing calculator. The parentheses are implicit with your old one.
Its - Possessive; It's - "It is" / "It has"; There - Location; Their - Possessive; They're - "They are"
October 26th, 2017 at 8:57:37 AM
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Apparently, "what is -2 squared?" is not the same question as "what is -2 x -2?"
DUHHIIIIIIIII HEARD THAT!
October 26th, 2017 at 9:03:14 AM
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My calculator is an HP 48GX scientific graphing calculator. Maybe it has to do with it being RPN?Quote: ahiromuMy guess:
Your 1995 calculator is probably a one line basic calculator (accounting calculator) and his 2017 calculator is a graphing calculator. The parentheses are implicit with your old one.
"Dealer has 'rock'... Pay 'paper!'"
October 26th, 2017 at 10:50:21 AM
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Quote: IbeatyouracesApparently, "what is -2 squared?" is not the same question as "what is -2 x -2?"
See I don't get that because that's EXACTLY what squaring is...
But from what I hear, math has "changed" since I learned it so who knows what the heck is going on.
October 26th, 2017 at 1:01:23 PM
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I think the wording stinks. When I hear "negative 2," this is on the number line two spots left of zero. That number squared is 4.
But, in an equation like 7-2^2, it's obvious that this is 3, not 11.
But, in an equation like 7-2^2, it's obvious that this is 3, not 11.
I heart Crystal Math.
October 26th, 2017 at 1:42:27 PM
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Quote: RSI'd say "negative two squared" is four. If you want the answer to be negative four, then ask "what is the negative of two squared?"
Ultimately, it comes down to: What is being squared? Two or negative two?
Better yet, do what I do, and always use parenthesis when something isn't obvious, to show order of operations.
Both of these are prime examples of my college stat professors favorite quote: "Figures never lie, but liars sometimes figure." You can make things ambiguous by not using the proper verbiage/signage when it comes to math.Quote: CrystalMathI think the wording stinks. When I hear "negative 2," this is on the number line two spots left of zero. That number squared is 4.
But, in an equation like 7-2^2, it's obvious that this is 3, not 11.
If we're reading the question as "What is negative 2 squared?" then the answer is clearly 4. (-2)^2. However if someone wanted to play with semantics they could try to relay the question as -(2^2) = -4. Order of operations are important, as well as verbiage because the proper verbiage tells you where to put the emphasis (parenthesis).
Playing it correctly means you've already won.
October 26th, 2017 at 2:48:43 PM
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I'm in the 4 camp.
I think both camps can agree the disagreement is a matter of semantics. If you wanted to know the answer to - (2^2), I think you should phrase it in English something like, "What is negative one times two squared?"
I think both camps can agree the disagreement is a matter of semantics. If you wanted to know the answer to - (2^2), I think you should phrase it in English something like, "What is negative one times two squared?"
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
