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Add Forum to Favorites | Send Topic To a Friend | View Forum FAQ | Track this topic Page: 1 2 3 »» |
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idinkin Member since: 4/9/2002 From: Kefar sava, Israel |
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 Posted - 6/29/2003 5:06:06 PM |
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| Hello everybody! Can you tell me please if a square root of a natural number may be negative? Thanx. |
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Ready4Dis Member since: 4/26/2002 From: USA |
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Posted - 6/29/2003 5:09:30 PM |
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| No, if you take the sqrt of a negative, it's an irrational number, but never negative. |
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Anonymous Poster |
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Posted - 6/29/2003 5:13:27 PM |
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| Actually, yes... every natural number has two square roots... the positive and negative "version" if you will. For instance, the square roots of 4 ar +2 and -2. The square root of a negative number is imaginary, not irrational. Irrational just means that the decimal part is neither terminating nor repeating. |
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Painless Member since: 2/7/2000 From: Finland |
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 Posted - 6/29/2003 5:24:43 PM |
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quote: Beep, wrong. A square root is defined to be positive. |
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Nervo Banned Member since: 3/29/2003 |
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Posted - 6/29/2003 5:39:07 PM |
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| I think you might be mis-interpreting the question. The orginal poster is asking about the square root of a natural number which is inherently positive. Of course you have a number that is both positive and negative. Remember solving quadratic equations where you used the formula and got 2 possible choices? |
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rohde Member since: 5/30/2002 From: Copenhagen, Denmark |
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Posted - 6/29/2003 5:41:50 PM |
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quote: No beep you. MathWorld -+-+-+-+-+-+-+-+-+-+-+-+-+-+- Any intelligent fool can make things bigger, more complex, and more violent. It takes a touch of genius -- and a lot of courage -- to move in the opposite direction. |
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DekuTree64 Member since: 8/30/2000 From: Kirkland, WA, United States |
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Posted - 6/29/2003 5:43:42 PM |
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quote: Anonymous is right, it can be negative. It's just the number you're taking the square root OF that has to be positive. If you take -2 * -2, you get 4, so it works. You can get different solutions to problems by working it twice, once with the positive sqrt and once with the negative, and they'll still work in the original equation. EDIT: Ack, 2 replies while I was typing that^_^; [edited by - dekutree64 on June 29, 2003 5:45:53 PM] |
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ApochPiQ Moderator - General Programming Member since: 7/17/2002 From: Atlanta, GA, United States |
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Posted - 6/29/2003 5:44:18 PM |
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quote: No, you're wrong. "The" square root, represented by the radical symbol, is defined as the positive second root. However, all numbers have two solutions to the equation x*x = n, and therefore two second roots: x = +- sqrt(n). |
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vanillacoke Member since: 2/19/2003 From: Chicago, US |
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Posted - 6/29/2003 5:44:41 PM |
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| There is a slight difference between the analytical square root function, and the plain ol' square root. It depends on which one OP was asking about, but chances are he doesn't really know. |
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Anonymous Poster |
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Posted - 6/29/2003 5:49:35 PM |
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| No, a square root can be negative. The square root of a positive number has two roots. These are called the positive square root and the negative square root. (imaginitive, i know) The square root of a negative number is imaginary. The number i is defined such that i*i = -1. Therefore the square root of 16 is -4 and +4, and the square root of -16 is 4i. |
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Cedric Member since: 3/13/2002 |
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 Posted - 6/29/2003 5:57:48 PM |
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Does it really matter? Why not wait for more information from the OP?quote: Such tact  |
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Mastaba Member since: 10/8/2001 From: Shreveport, LA, United States |
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Posted - 6/29/2003 6:02:12 PM |
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| It is really sad to see the number of people that don't know that the square root function is indeed DEFINED to always to be positive. So the sqrt(4) is always 2. It is only when you do a symbolic sqrt that you get 2 possible answers. Go ahead, try it. Load up Maple, or Mathematic and try solving for the sqrt of 4. It'll only give you 2 as the answer. Try the sqrt(x*x) and then you'll get -x and +x. |
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jamessharpe Member since: 1/6/2003 From: Bristol, United Kingdom |
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Posted - 6/29/2003 6:02:39 PM |
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quote: In fact the square root of -16 is 4i or -4i (the complex conjugate roots). |
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Cedric Member since: 3/13/2002 |
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Posted - 6/29/2003 6:19:09 PM |
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quote: Grrr... Read the MathWorld link. As vanillacoke said, a number may have multiple square roots ("symbolic" doesn't have anything to do with it). BUT, the square root FUNCTION is defined to be only the positive value (at least, in the reals). Of course, a function is a one-to-one mapping. It can't have multiple images for a given value. Cédric |
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vanillacoke Member since: 2/19/2003 From: Chicago, US |
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Posted - 6/29/2003 6:23:49 PM |
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| Cedricl, you took the words right out of my mouth. |
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Cedric Member since: 3/13/2002 |
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 Posted - 6/29/2003 6:27:03 PM |
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| Nyahaha! Fear the Gamedever who has nothing to do but click Refresh! |
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vanillacoke Member since: 2/19/2003 From: Chicago, US |
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Posted - 6/29/2003 6:30:30 PM |
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| I'm afraid, all right. |
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stevie56 Member since: 6/17/2002 From: Scotland |
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Posted - 6/29/2003 6:35:37 PM |
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| "Can you tell me please if a square root of a natural number may be negative?" No mention of a FUNCTION defined anywhare in MATHEMATICA or anywhere else is referred to by the question. So, the answer to the question that was actually asked is YES. You may define what you like in your software tools, but mathematical questions deserve mathematical answers. Stevie Don't follow me, I'm lost. |
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idinkin Member since: 4/9/2002 From: Kefar sava, Israel |
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Posted - 6/30/2003 12:59:54 PM |
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| So... What I understand from this discussion is: The square roots of 4 are -sqrt(4), sqrt(4). So square root is always positive. If I'm wrong tell me where my mistake is? [edited by - idinkin on June 30, 2003 1:00:31 PM] |
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Nervo Banned Member since: 3/29/2003 |
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Posted - 6/30/2003 1:10:48 PM |
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| idinkin you are correct. The square root of 4 for instance is sqrt(4) and -sqrt(4) with answers 2 and -2. Therefore it is a combination of two functions just like for example graphing a circle with x^2+y^2=r^2. It would like like a parabola placed on its side. [edited by - nervo on June 30, 2003 1:11:31 PM] |
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idinkin Member since: 4/9/2002 From: Kefar sava, Israel |
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Posted - 6/30/2003 1:12:33 PM |
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| OK. Thanx! |
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JohnBolton Member since: 4/3/2002 From: Belmont, CA, United States |
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Posted - 6/30/2003 2:03:08 PM |
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quote: Not quite, but let me try to end this silly thread. "square root": The following statement can be accepted as true: The square roots of a positive number n are sqrt(n) and -sqrt(n).Anyone that doesn't accept that statement is just quibbling over the meanings of some terms. If you (or anyone else) accept that statement, then you must agree with this statement: There are two square roots of a positve number - one is positive, one is negative. sqrt(), the C function: According to the C standard, sqrt() return a positive value or 0 if the parameter is not negative. The square root symbol: As far as I know, the sign of the value of the square root symbol depends on the context. I've seen it written with "+/-" and without. Generally, when it doesn't have "+/-", the author assumes you know whether he means both roots or just the positive root. I don't know if there is a notation standard for it, but that is what I've seen. I hope that answers your question, once and for all. If the definition of the term "square root" is really what you want then look it up in an authoritative source and ignore anyone here that does not quote directly from an authoritative source. |
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Mastaba Member since: 10/8/2001 From: Shreveport, LA, United States |
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Posted - 6/30/2003 2:49:52 PM |
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| It isn't really quibling. It is a fact. The square root of 4 is 2. Plain and simple. However taking the equation X^2-4=0, and solving that for x requires you to take the square root of AN UNKNOWN. That is why you get 2 answers here. Because you don't know which answer is the correct answer (they may both be correct, or maybe only one is correct in a given context). |
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Dracoliche Member since: 7/24/2001 From: Australia |
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Posted - 6/30/2003 3:21:58 PM |
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quote: /me tries to make a joke about religion and mathematics. |
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JohnBolton Member since: 4/3/2002 From: Belmont, CA, United States |
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Posted - 6/30/2003 3:24:39 PM |
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quote: I can't believe I'm responding... So what you are saying is that -2 is not a square root of 4 and thus (-2)*(-2) is not 4. If you aren't saying that, then we are definitely quibling over the definition of "square root". Here is my definition of square root: If y = x2, then x is a square root of y.This seems like a reasonable and effective definition, but you say it is wrong. Please tell me where I can find out what the correct definition of "square root" is, rather than just taking your word for it. |
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