|Nth root has been listed as a level-3 vital article in Mathematics. If you can improve it, please do. This article has been rated as B-Class.|
|WikiProject Mathematics||(Rated B-class, Mid-importance)|
- 1 .
- 2 Merge
- 3 Pronunciation?
- 4 Simplifying Radicals
- 5 Finding all roots
- 6 Fifth root extraction
- 7 Only for reals
- 8 Are "almost all" square roots of rationals irrational?
- 9 Solving Polynomials
- 10 Arabic
- 11 EXTERNAL LINKS
- 12 Problem with infinite series
- 13 Charles T. Gidiney
- 14 Simplified Form
- 15 Zeroth root?
- 16 non-integral roots
- 17 Restrictions
- 18 There is no mentioning of why it's called the nth root.
- 19 Graph
"Quantities left uncomputed under a radical sign are also called surds." This is not correct. Surds are strictly irrationals.
This article talks about "surds" before defining what they are. - dcljr 06:03, 6 Aug 2004 (UTC)
This article also perports to define the term radical, and at no point does it directly do so. - Preceding unsigned comment posted by 184.108.40.206, April 10, 2006.Cliff (talk) 06:28, 22 March 2011 (UTC)
The section, 'Finding all the roots', tells us how to find all the roots in terms of the principle root and n, but the only definition for the princinple root used in the article is the one which is always a real number and doesn't always exist. Someone needs to put in a bit about the extension to complex numbers. There is actual more on the cube root page. - Preceding unsigned comment posted by 220.127.116.11, May 26, 2006.Cliff (talk) 06:28, 22 March 2011 (UTC)
I think this article and N-th root are the same thing, just under different names!
shouldn't the equation for finding the nth root be on this page?? 'twould be useful to say the least (not to mention relevant)
Edit: Simon Fendall This relates to the merge somewhat. When visiting the N-th Root this does not exist, but when visiting the Nth Root under surds it shows Which appears to be wrong. —Preceding unsigned comment added by 18.104.22.168 (talk) 22:24, 3 March 2008 (UTC)
I believe this page would be beneficial if it also contained correct pronunciation examples of nth roots.
For example, how do you say 4√200 ? I believe the only correct way to say it is 200 to the fourth root, however maybe some could clarify this.
I added some information related to finding products and quotients of radicals w/ different indices and how to simplify indices. I believe the examples I used are correct, if not my apologies and permission (request) to change it ASAP. Nevertheless, I am not quite sure I have written in the correct section. Should it be moved to the section dealing with surds, or should it remain in the 'basic operations' section? -- Ishikawa Minoru 22:06, 7 June 2007 (UTC)
Finding all roots
The formulas for finding the roots in the article are confusing. What is given in the article is not really an equation, as it has no result (i.e., it is merely an expression). Further, having appear in the formula is confusing, as that is the result one is trying to find. Should the formula rather be written as the following (guessing), like it is in Nth root algorithm?
Also, φ and the "Euler's equation form" should really be defined/expressed in the article. Readers shouldn't have to do this level of research in order to understand an encyclopedia article. SharkD (talk) 08:10, 20 February 2008 (UTC)
- This section is about as clear as mud, but if there were any mathematicians reading this, they'd simply criticize your education for your ignorance of Euler's formula and how it should be interpreted when it appears in aeiφ In Euler's formula, φ is defined as being equal to "atan2(y,x)", where y is the imaginary part of a complex number z, and x is the real part of z. It is far from clear whether z should be replaced with a in this incarnation of the formula, or whether z is some variable that has nothing whatsoever to do with a. It is also not clear whether the formula aeiφ really works for real numbers, since Euler's formula is clearly meant to be used for complex numbers.
- As for appearing in the definition, the algorithm requires the principal nth root of a as an input (use Nth root algorithm to find that root). The algorithm being defined merely finds the other nth roots.
Fifth root extraction
Only for reals
This identity does not work for non-real complex numbers:
- in some sense of the word, 2i+2 is a "positive" complex number, residing in the first quadrant of the complex plane. Three of the four quadrants can be considered to be positive depending on context. Positive is quite ambiguous and does not imply a real number. Cliff (talk) 15:27, 22 March 2011 (UTC)
- Not in any useful or standard sense of the word, because (2i+2)5 = -128 - 128i, and you have the unfortunate spectacle of a power of a "positive" number becoming "negative". There is no way to categorise general complex numbers as positive and negative that always respects the laws positive x positive = positive etc. To a mathematician, "positive number" always implies that the number is real. Gandalf61 (talk) 15:53, 22 March 2011 (UTC)
- Not all readers of this page are mathematicians. In fact, I'll guess that of the people who search for this page and find it, most are not mathematicians. To the general reader, positive only means "not having a negative sign". For instance, if you asked the general reader whether -y is positive or negative, the answer would almost universally be "negative", ignoring the actual value of y. Thus, the minor addition to the section in question. Cliff (talk) 17:08, 22 March 2011 (UTC)
Are "almost all" square roots of rationals irrational?
Off the top of my head, it seems that square roots of irrationals must be irrational themselves, because if the root were rational the numerator and denominator could be squared to give a rational number (and we've already said the original must be irrational). However, what about the rationals? Assume a rational number x = a/b, in lowest terms. Here's what I come up with:
1) Sqrt(x) will be rational if and only if sqrt(a) and sqrt(b) are rational. 2) Square roots of integers such as a and b are rational if and only if the number is a perfect square. 3) Perfect squares are in a one-to-one correspondence with the natural numbers, as every natural number has a perfect square and there are no perfect squares which are not the square of a natural number. 4) We can safely limit the discussion to whole numbers, as the case x = 0/b is trivial and x = a/0 isn't within the domain of algebra, and all negative numbers would have the same square as their positive counterpart.
Ultimately, then, the question is: Given two coprime whole numbers a and b, what are the odds that both of them are perfect squares? Have I missed anything, and is the answer to the above question known? 22.214.171.124 (talk) 23:45, 11 April 2009 (UTC)
- Of course, the answer is known. This is really a trivial problem. Suppose x=a/b where a and b are integers and b>0. Then x=a·b/(b2). So x is the square of a rational number if and only if a·b is the square of an integer. JRSpriggs (talk) 05:40, 12 April 2009 (UTC)
In the Solving Polynomial section, the link to elementary operations currently redirects to elementary matrix. I am not an expert in the subject, so such a redirection may be completely expected to one versed in mathematics, however, my expectation of the link based on its title alone would yield the "elementary operations" of Arithmetic. I suspect that the link may have been added before a move or without verification of the linked content. If the current link is most appropriate, I might suggest changing the linked text to "elementary matrix operations" or something similar.
- You're right, it does indeed refer to the elementary operations of arithmetics. Thanks for bringing this to our attention; I now changed it to point to elementary arithmetic. Cheers, Jitse Niesen (talk) 16:11, 29 June 2009 (UTC)
The article says:
- the first letter in the word (Jathir, [with the "th" pronounced like the "th" in the english word "the"] in Arabic means root)
I think that it is not exact.
I wonder what makes a person so "priviliged" that his/her external-link is allowed to appear at wikipedia. I mean, if Wikipedia does not like EXTERNAL LINKS then WIKIPEDIA SHOULD NOT mantain the external-links section. I think it is an obvious public-outrage for many people to realize that only two or three guys are "priviliged" by wikipedia, i do not see any justice on that. Wikipedia should either mantain the EXTERNAL LINKS in another related page or definitely eliminate all of them. What makes some few guys so "privileged"? What makes some guy to be the judge for selecting only two or three external links? Mirificium (talk) 22:34, 20 March 2010 (UTC)
- The single entry there doesn't add anything extra to the article so I'll delete it, so yes they'll all disappear! That's simply because nobody has added anything with extra encyclopaediac content. Thanks for pointing it out. Dmcq (talk) 09:57, 18 March 2011 (UTC)
Problem with infinite series
The following was added to the infinite series section or using this formula
- Mathematical Hand Book of Formulas and Tables , Murray R.Spiegel, phd. john liu, phd
I checked an early version of that book and have not been able to find the series formula. In fact I believe that series is an editors own work putting two other things together. I am not saying it is false but I simply do not believe it has been established that the formula is important enough to be included which is what the citation is needed for. I will delete the formula in a few days if no proper citation with page number to something very similar is forthcoming. Dmcq (talk) 11:45, 1 October 2012 (UTC)
Charles T. Gidiney
I have added Gidiney to the history section, but I plan to explain his contribution further. His contributions are little-know, but key--the type that often goes unnoticed. If there is disagreement with his inclusion or a suggestion, please, let me know. I seek to reach consensus. Historian (talk) 02:31, 14 June 2014 (UTC)
I don't want to change sourced text in a way that contradicts cited source, however I believe one needs another criterion along the lines of:
- 4: Doesn't contain a product of radicals.
Would it be useful to state explicitly that there are no zeroth roots for real or complex numbers (since such a thing involves undefined division by zero)? The article states in several places that for the nth root of x, n is a positive number, but some people may take that to mean that n is any non-negative number, which includes zero. — Loadmaster (talk) 18:22, 13 January 2015 (UTC)
- Um. There's been trouble at exponentiation over 0^0 you might want to ignore the problem! We shouldn't have anything in unless there's some book or paper that describes it. Dmcq (talk) 18:43, 13 January 2015 (UTC)
Something can be said for where x is not a positive integer, but when actually used, it is almost always a positive integer. For general non-zero x,
I fail to see why nth roots have to be arbitrarily restricted to n being positive integers. The concept works with any nonzero complex number. Scientific calculators accept values of n which are not positive integers (calculating on a scientific calculator yields 0.5)- Michael Ejercito — Preceding unsigned comment added by 126.96.36.199 (talk) 18:01, 2 February 2015 (UTC)
- One could make a point for negative integers, as the changed definition is trivial. However, general real (or complex) numbers should just refer to the article exponentiation, with all its disputes and multiple definitions, except the 00 dispute. — Arthur Rubin (talk) 02:05, 4 February 2015 (UTC)
Why does n have to be an integer for this operation to be valid?? In other words, why don't we define "1.5th roots"?? We do define a 1.5th power, so why can't we define a 1.5th root?? Georgia guy (talk) 20:45, 23 March 2016 (UTC)
There is no mentioning of why it's called the nth root.
I tried to improve the article by adding why it's called the n'th root, but this was reverted on the grounds that it was redundant. I've read through the article once more, and is unable to understand where this is mentioned. Please point out the redundancy. BFG (talk) 15:47, 19 March 2018 (UTC)
- The redundancy is adding a second formula whose content is already expressed in the immediately following formula. Your edit also fragmented the first sentence, leaving the first paragraph in a broken state.
- The etymology of the word "root" would certainly be an interesting thing to add to this article, with appropriate historical/linguistic sources. (There is already a discussion of related terms, like "surd".) However, you're proposed etymology ("nth root" <- "root of a polynomial equation") is almost certainly backwards: it seems far more likely to me that the path is "square root" -> "nth root" -> "root of a polynomial equation". Of course if you had a proper source for your version, I would be more than happy to revise my view and find a way to include it in the article. --JBL (talk) 17:20, 19 March 2018 (UTC)
- May I second the etymological direction towards the polynomial roots? I just want to add the exponential in parallel to a chain starting with root, the corresponding terms establishing their respective inverses: 2nd power(=square) <-> square root (=2nd root?), 3rd power(=cube) <-> cube root (=3rd root), ... n-th power <-> n-th root. Imho, this relation ("is the inverse to") between n-th power and n-th root is sufficiently addressed. Purgy (talk) 18:20, 19 March 2018 (UTC)
- The term root comes from radix(latin for root) radix and was used for the unknown e.g. x, when translating arabic texts to latin. Square root is thus the second power of the unknown (x2) cube root the 3rd power of the unknown(x3) and so on. I've probably read this in a math textbook at some time, but I have no clue which. It'll take some time to figure it out where. BFG (talk) 19:05, 19 March 2018 (UTC)
- That's fine, it's a personal taste thing, not worth arguing about. If you do find the etymology somewhere, that would be a great addition to the section of this article that deals with the terminology (and, quite possibly, to the other related articles square root, cube root, root of a function. (Probably, it does not belong in the first sentence of any of these articles, though.) --JBL (talk) 19:14, 20 March 2018 (UTC)
- I've already figured out the original source. It's in one of the translations of Euclid's Elements to Latin. Probably the Bartolomeo Zamberti translation. I'll try to get a hold of it as soon as possible. BFG (talk) 06:50, 21 March 2018 (UTC)
- Reviel Netz, The Transformation of Mathematics in the Early Mediterranean World: From Problems to Equations, p. 138
The graph at the top of the article, Image:Roots chart.svg, is peculiar. It shows the values of the nth roots of the integers connected by straight lines between the integers values. Two problems:
- Why is it restricting itself to integer values?
- What is the meaning of the linear interpolation between the integer values?
- Macrakis I agree that the graph is not very good, but I think your new caption is wrong about what the graph shows. The inset caption is correct: each colored line shows the successive roots of a given integer. For example, the top-most teal line is at height 10 for x = 1 (because the 1th root of 10 is 10), then it is at height 3-point-something for x = 2 because the square root of 10 is 3-point-something, then it is at height 2-point-something for x = 3 because the cube root of 10 is just a smidge larger than 2, and so on. I propose getting rid of the figure and replacing it with something more informative. --JBL (talk) 18:52, 20 March 2018 (UTC)
- I think something like the upper half of File:Mplwp_roots_01.svg used in Exponentiation#Rational exponents, possibly with modified labels, would do the trick nicely. The current pic might serve best in illustrating some asymptotic behaviour (n to \infty). I regret not being versed in searching for pics. Purgy (talk) 07:25, 21 March 2018 (UTC)