What is Root: Definition and 941 Discussions

In vascular plants, the roots are the organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They most often lie below the surface of the soil, but roots can also be aerial or aerating, that is, growing up above the ground or especially above water.

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  1. S

    Can Non-Diagonalizable Matrices Have Square Roots?

    Hey all, I've run into a snag with research and it is partly related to taking the square root of a matrix. I've seen related stuff concerning matrices that can be diagonalized, however the 2x2 matrix in question is not diagonalizable. Can the square root of such a matrix be determined? If...
  2. B

    Number Theory: nth root of n is irrational

    1. For n ≥2, n^(1/n) is irrational. Hint provided: Use the fact that 2^n > n2. This is probably familiar to many. By contradiction, n = a^n/b^n --> a^n = n(b^n) --> n|a^n --> n|a Am I trying to force the same contradiction as with 2^1/2 is rational, that is, that a/b are not in lowest terms? Or...
  3. B

    Show the Cube root of x is uniform continuous on R.

    Homework Statement Let f(x)=x^{1/3} show that it is uniform continuous on the Real metric space. Homework Equations By def. of uniform continuity \forall\epsilon>0 \exists\delta>0 s.t for \forall x,y\in\Re where |x-y|<\delta implies |f(x)-f(y)|< \epsilon The Attempt at a Solution...
  4. M

    Find the Proof: Tangent Lines & a Circle w/ Square Root of 3 Radius

    Homework Statement Our teacher was talking about something regarding two tangent lines on a circle who distance between the tangent lines is square root of 3 times the radius of the circle... She wanted us to find the proof of this but I am stumped on where to even look... Does anyone know...
  5. Y

    Function involving a negative square root HELP?

    As you can't take the square root of a negative number without introducing complex numbers, which would be the correct answer to this function: Equation: x = -2 f(x) = √x / (x(x-1)) Answer a) 1.41i / 6 or Answer b) 0
  6. M

    How to know which sign of root to take when finding the inverse of a function

    Homework Statement find the inverse of y=2x^2-8x x>=2 I am in calculus b but forgot some of the algebra so I am not sure how to treat the root Homework Equations The Attempt at a Solution I am skipping steps y=2(x-2)^2-8 (y+8)/2=(x-2)^2 I know that x >=2 so f(2) =-8 and...
  7. JeremyEbert

    Simplifying Square Roots: Unraveling the Mystery of the Square Root Function

    Is there a way to simplify this? Is this a known function? tan(arccos(((x/y)-1/y )/ ((x/y)+ 1/y)))*((x/2)-1/2)=sqrt(x)
  8. P

    Proving Root n is Irrational: Perfect Square Affects Proof

    How to prove that root n is irrational, if n is not a perfect square. Also, if n is a perfect square then how does it affect the proof.
  9. P

    Cube root of 6 is irrational. (please check if my proof is correct)

    Prove that cube root of 6 irrational. Solution: I am trying to prove by contradiction. Assume cube root 6 is rational. Then let cube root 6 = a/b ( a & b are co-prime and b not = 0) Cubing both sides : 6=a^3/b^3 a^3 = 6b^3 a^3 =...
  10. JeremyEbert

    Understanding E8 Root Systems: A Comprehensive Guide to Prime Roots and Patterns

    I'm trying to understand root systems better. They seem to be tied to what I've been working on. Any suggestions on books? here is an e8 root system http://upload.wikimedia.org/wikipedia/commons/thumb/f/fe/E8_graph.svg/500px-E8_graph.svg.png here is some of my root system. the prime...
  11. J

    Why the Square Root of 3 in 3-Phase Voltage Drops?

    Banging my head against a wall trying to prove to a coworker why the square root of three shows up in a three-phase voltage drop calculation...any ideas?
  12. D

    Proving Primitive Root of Unity: z = cos(2pi/n) + isin(2pi/n)

    Homework Statement show that cos(2pi/n) + isin(2pi/n) is a primitive root of unity Homework Equations The Attempt at a Solution if i know z = cos(2pi/n) + isin(2pi/n) is an nth root and I'm trying to prove that z is a primitive nth root. is it correct to assume that z^k is not...
  13. JeremyEbert

    Geometric construction of the square root

    Is anyone familiar with this method of determining square roots? http://www.cs.cas.cz/portal/AlgoMath/Geometry/PlaneGeometry/GeometricConstructions/SquareSquareRootConstruction.htm I have an equation that I'm working on that expands on this a bit and I'd love some feedback.
  14. R

    Finding the Alternate Form of a Square Root: A Mathematical Challenge

    Hey there, Square roots never have been my strongest point in maths, but I'm not seeing the trick in this example: I'm trying to find an alternate form of: sqrt(3+sqrt(8)) I get as far as: sqrt(3+2 sqrt(2)) But i know i want to/should end up with: 1+sqrt(2) I just don't know how...
  15. R

    Construct geometric line with nested root

    well it is easy to construct sqrt(2) with a triangle with two sides of length 1. but what about sqrt(2 + sqrt(2)) or the iteration sqrt(2 + sqrt(2 + sqrt(2))). the question is how to construct a line with length sqrt(sqrt(2)) i guess(beginning with lines of length 1), but i am not sure.
  16. S

    Indefinite integral for the square root of a quartic function

    I arrived at this problem while trying to find the length of a 3D http://en.wikipedia.org/wiki/Cubic_interpolation" . Basically, I'm having to figure out how to integrate ((At4+Bt3+Ct2+Dt+E)1/2)dt A,B,C,D, and E are constants which have to be plugged in after integration, I'm sorry to say...
  17. D

    Root mean square speed of helium atom

    Homework Statement Helium is used to fill a balloon of diameter 44 cm at 22 degrees C and 0.9 atm. The mass of a helium atom is 4.0026 u, the conversion factor from u to kg is 1.66 x 10^-27 kg/u, the conversion factor from atm to Pa is 1.013 X 10^5 Pa/atm, the universal gas constant is...
  18. K

    What are the roots of x^(p-1) in Z_p?

    Let p be a prime number. Find all roots of x^(p-1) in Z_p I have this definition. Let f(x) be in F[x]. An element c in F is said to be a root of multiplicity m>=1 of f(x) if (x-c)^m|f(x), but (x-c)^(m+1) does not divide f(x). I'm not sure if I use this idea somehow or not.
  19. Z

    Domain of a quadratic function under square root having no x intercept

    I am trying to find the domain of this function f(x)=sqrt(x^2 - 2x +5). i am supposing that y=x^2 - 2x +5 and y must be greater of equal to 0. in otherwords where the graph is touching or above x axis. to find where the graph is touching x-axis i am trying to find the x intercept and i get...
  20. Z

    Why is one root rejected when solving equations with multiple solutions?

    When we solve to equations say y2 = 4x and x2 + y2 = 9/4 for x, we get two values - x=0.5 and x=-4.5 The equations represent a parabola and a circle resp. with x=either 0.5 or -4.5 as the abcissae of intersection. I don't understand why do we reject one value which is -4.5 in this case...
  21. C

    Square root of complex number in rectangular form

    Homework Statement I don't know how to find the square root of a complex number in rectangular form? As in, say, \sqrt{}9-6i..my calculator can't do such an operation (yet my graphics calculator can, which can't be used in exams), so how do i go about to do this 'by hand'? I just found...
  22. H

    Is an irrational root of a real number imaginary or real?

    We can easily comment the result of a root operation just by the information if the degree of the root is odd or even. But what if the degree of the root (or power) is irrational? For example; -64 ^ \frac{1}{2} \, = \, j8 \,\,\,\,\, (imaginary) -64 ^ \frac{1}{3} \, = \, -4 \,\,\,\,\...
  23. H

    Algorithm to calculate root (or power) in computer

    I need an algorithm to calculate nth root or power of any given real number. "n" can be either integer or fractional, and is real. I found http://en.wikipedia.org/wiki/N-th_root_algorithm" , but it requires to calculate power in it, therefore I can't use it. Newton's method: x_{k+1} =...
  24. C

    Calculate Root Mean Square Speed of Oxygen Molecule in a Flask

    I solved on my own the work below is incorrect.Homework Statement A sealed 500ml flask contains oxygen gas at a temperature of 27 degrees Celsius. a) Calculate the root mean square speed of an oxygen molecule in the flask? b) Calculate the average kinetic of an oxygen molecule in the flask...
  25. D

    Wolfram answer for cubed root of -1

    At http://www.wolframalpha.com/ , if you type: 1) (-1)^(1/3) It gives a complex approximation. Isn't it exactly -1? David
  26. A

    Proving at Most One Real Root of x³-15x+C in [-2,2]

    Homework Statement Show that the equation x3-15x+C=0 has at most one real root in [-2,2] Homework Equations Rolle's Theorem, and Intermediate Value Theorem. The Attempt at a Solution I showed that there is a root in [-2,2] by use of Intermediate Value Theorem. f(-2)<0 f(2)>0...
  27. S

    Graph/analyze a function of a rational /w complex root?

    graph/analyze a function of a rational /w complex root?!? Homework Statement The function is y=x^2/(x^2+3) Homework Equations First and Second Derivatives Chart to find intervals of increase/decrease and concavity. The Attempt at a Solution 1) Domain {XeR} 2) Intercepts If...
  28. X

    A is a root of order of polynomial p iff p(a)=p'(a)= =[p^(k-1)](a)=0

    a is a root of order k of the polynomial p provided that k is a natural number such that p(x)=[(x-a)^k]r(x), r is a polynomial and r(a) not equal to 0. Prove a is a root of order k of the polynomial p iff p(a)=P'(a)=...=[p^(k-1)](a)=0 and [p^(k)](a) not equal to 0. Note: [p^(k-1)](a) :=...
  29. L

    C/C++ How do you superimpose graphs from different root files in C++/root

    Hi, ive created several graphs in different emacs files. I now want to superimpose them using code in a different emacs file. This is what i have done: //get the input files TFile * inputfile = new TFile("p60.root","READ"); TFile * inputfile2 = new TFile("p20.root","READ")...
  30. C

    Integrating a strange square root function

    Homework Statement Calculate the area under the curve for the following: f(x) = √x*√(−32 − x) and g(x) = √(−x2 − 32x) Homework Equations The Attempt at a Solution I've been trying to do partial integration since the functions f(x)=g(x)area are mirrored, so they are equal...
  31. S

    Proving the Existence of Exactly One Real Root for 2x-1-sinx=0

    Homework Statement * Show that the equation 2x-1-sinx=0 has Exactly one real root. Homework Equations *N/A The Attempt at a Solution *Ok so normally to find the real roots for x I would solve for x when I set the function equals to 0, but with this function there is an x...
  32. Ivan Seeking

    Maca Root - fireworks in your pants?

    http://www.macasex.com/ I saw a bit about this on TV [an investigative report, not a commercial] the other night. Apparently it is common for women in Peru to use Maca root to increase libido. When asked if it works, one women commented, "It will make Chinese fireworks in your pants!". It...
  33. L

    Comp Sci Drawing a graph using C++ / ROOT (CERN)

    Homework Statement Im having difficulty drawing a specific graph. I am not entirely sure how to explain my question/ the graph i need to draw so i think the best way is to provide a bit of my code and explain using it the graph using it... the code below gives a read out of the energy...
  34. L

    Help needed with plotting a graph (cern ROOT)

    ive been plotting 2D histograms (x vs y). when plotting using Draw->("surf"). it gives a 3D plot, showing the varying number of "hits" in each bin. I want to draw a TGraph which represents this so when drawing x vs y using Tgraph it gives a continuous line instead of a bunch of dots. I've got...
  35. H

    Parameters for Root Locus Method using Lead Compensator

    Hi everyone, I would please like some suggestions regarding where my error is, designing a lead compensator with the root locus method for a unity feedback control system where G = [12.5] / [2.5 1 2500]. I want to set the overshoot zeta = 0.5 for an overshoot of 16%, and settling time Ts =...
  36. N

    Complex Numbers: nth Root Proof

    Homework Statement Really new to complex numbers so please forgive my ignorance. Prove that if the complex number z is an nth root of the real number x then the complex conjugate z (z with horizontal line on top) is also an nth root of x.Homework Equations i2=-1The Attempt at a Solution nsqr(z)...
  37. J

    Find polynomial when given a complex root

    Hi there, I have over the last couple of month worked my way through Algebra Demystified and College Algebra Demystified (well almost), and I just completed the chapter on polynomial functions and I’m stuck at one of the questions in the chapter review where I’m given a complex root and the...
  38. J

    Integral of a function with a square root in denominator

    Homework Statement integrate (xdx)/sqrt(1-x^2) on the integreal [2,5] Homework Equations integral u^n(du) = u^n+1/(n+1) The Attempt at a Solution I'm no good at using latex so I scanned in my work. I get .716 but when I check with my calculator it comes out as 2.863
  39. R

    Two formulas for calculating root of a complex number in a exponential form

    z_k=\sqrt[n]{u}=\sqrt[n]{r}e^{i\left(\frac{\phi+2k\pi}{n}\right)}, k=0,1,2,...,n-1 and z_k=\sqrt[n]{u}=\sqrt[n]{re}^\frac{\phi+2k\pi}{n}, k=0,1,2,...,n-1 Which one is incorrect (note that in the first, e is out of the root)?
  40. R

    What is the Antiderivative of a Complex Square Root Function?

    Homework Statement Antiderivative of sqrt[e^x+ln(x^2)+1] Homework Equations The Attempt at a Solution (2[(e^x+ln(x^2)+1)^(3/2)]x^2)/[3(e^x+2x)]
  41. B

    Troubleshooting Differentiation of x over Root x

    I tried to use tex code but it seems to be caching the image on preview, so anyway dy/dx ( x / root x) = 1 / ( 1/2 x^(-1/2) ) however the answer given to me is just ( 1/2 x^(-1/2). What's gone wrong? Spent an hour on this and now unsure if my algebra is wrong. And the tex code that I...
  42. Femme_physics

    Square root of 4.1- do you have to use calculus?

    Square root of 4.1-- do you have to use calculus? In order to solve square root of 4.1, is there a simple arithmetic method or do you have to use calculus and use that "tangent line approximation formula"? I wonder how do calculators do it... does anybody know?
  43. P

    How Do You Calculate the Square Root of a Polynomial?

    does anyone know any specific method to find the square root of a polynomial like : 4x4 + 8x3 + 8x2 + 4x+ 1 ?? thanks in advance!
  44. L

    2nd order homogeneous equations complex root

    Homework Statement y'' -2y' +5y =0 , y(0)=1, y'(0)=1 you get a complex root conjugate. Homework Equations y=e^(rt) y'=re^(rt) y''=r^2 * e^(rt) The Attempt at a Solution I have in my notes sin(omega*t)e^(sigma *t), cos(omega *t)e^(sigma). I don't think i took down the notes...
  45. ╔(σ_σ)╝

    Proof of the irrationality of the square root of primes ?

    Homework Statement If p is prime \sqrt{p} is prime. Are there flaws in my proof ? Homework Equations The Attempt at a Solution Assume \sqrt{p}=\frac{m}{n} and gcd(m,n)=1 p = \frac{m^{2}}{n^{2}} Since p is an integer n^{2}|m^{2} but gcd(m,n)=1 Therefore...
  46. A

    Proving that n-th root of n is irrational

    Homework Statement if n>1, prove that \sqrt[n]{n} irrational Homework Equations n/a The Attempt at a Solution so suppose it is rational, so i know \sqrt[n]{n} must be integer, say p then n=p^n and how do i prove this is not true?? i can prove if p>1 then p^n>n for all n>1 by induction...
  47. E

    Proving limit of the nth root of n

    Homework Statement Prove the following limit: lim_{n \rightarrow \infty } n^{ 1 / n } = 1 Homework Equations Not sure. The Attempt at a Solution Given any \epsilon > 0, choose N \in \mdseries N s.t. \left| n^{ 1 / n } - 1 \right| < \epsilon for all n > N I am not sure...
  48. B

    Definite Integral (Square Root)

    Homework Statement [PLAIN]http://www4a.wolframalpha.com/Calculate/MSP/MSP184619c56eg84971107d00001e292h4340heh8g4?MSPStoreType=image/gif&s=35&w=135&h=53 It is a definite integral between x=0 and x=20. I forget how to integrate with a square root. Do you just change it to a power of a...
  49. K

    Square root integration problem

    Homework Statement Integrate : f(t) = t3/ sqrt(t2+1) Homework Equations The Attempt at a Solution t2* t / sqrt(t2+1)let u = sqrt(t2+1) u=(t2+1)0.5 u2 = t2 +1 t2 = u2 -1 -Eq 1u=(t2-1)0.5 du = t/sqrt(t2-1) dt dt = sqrt(t2-1)/t du -Eq 2 Hence Substituting 1 and 2...
  50. S

    How to integrate a function within a square root

    Homework Statement Find the length of x=y^3/30+5/(2y) on 3 <= y <= 5 Homework Equations L = integral sqrt(1+(dx/dy)^2)dx The Attempt at a Solution I got to the integral upper bound = 5, lower bound = 3, sqrt(y^4/100+25/(4y^4)+1/2)dy. How do I actually solve the integral? It...
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