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. Z

    Solving 4th Order Diff. Eq. with Complex Root: Daunting Task?

    I have a 4th order differential equation with given -2 +3i root. Now need to find the homogenous solution. Well, if the root was real, it would be easier but now I'm stuck and don't know how to proceed. What am I supposed to do to solve this ? Equation is : d4y(t)/dt4 +6d3y(t)/dt3 +...
  2. W

    Installing ROOT in ubuntu 11.10

    when installing ROOT in ubuntu 11.10 i have the following message name@ubuntu:~/root$ ./configure Checking for source directory ... /home/waleed/root Configuring for linuxx8664gcc Checking for GNU Make version >= 3.80 ... ok Checking for C compiler ... gcc Checking for C++ compiler ...
  3. I

    MHB N th root of a positive number is positive ....

    Hi Let \( c>0 \) be a real number. Then I am trying to prove that \( \forall\; n\in\mathbb{N}\; (c^{1/n} >0) \). I let \(n\) be arbitrary and then tried to use method of contradiction. But ran into difficulties. Is there another approach ?
  4. H

    Square Root of an Irrational Number is Irrational

    Homework Statement Let a be a positive real number. Prove that if a is irrational, then √a is irrational. Is the converse true? Homework Equations So, an irrational number is one in which m=q/p does not exist. I understand that part, but then trying to show that the square root of an...
  5. H

    Prove a Sum is Larger than a Root

    Homework Statement Let nεZ>0. Prove that: Ʃ1/√(i) ≥ √(n) The Attempt at a Solution I'm not sure where to begin, this feels like it should be an induction problem, but I'm not sure how to show that √(n) + 1/√(i+1) ≥ √(n+1). There doesn't seem to be any obvious algebra that would...
  6. A

    How Do You Calculate Root Mean Square Uncertainty?

    Root Mean Square Uncertainty [solved] My TA gave us a paper after this assignment regarding how to do Root Mean Square Uncertainty, however I can't read her handwriting... I think I get the gist of it, but It's written so strange I need to check. Is it sqrt(...
  7. K

    Assignment question, root, Intermediate Value Theorem

    Homework Statement Prove that Prove that the equation has at least one positive real root, using the Intermediate Value Theorem on an appropriate function. 3 arctan(2x-1)=cos^2(x-(∏/6)) + 1 Homework Equations No clueThe Attempt at a Solution I honestly speaking have no clue how to even...
  8. S

    Factors affecting beet root cell membrane

    Hi. I am currently doing an experiment regarding to the factors affecting beet root cell membrane. Some of them are pH (2,4,6,8,10) , Ethanol (1%, 25%, 50%) and Detergent(1%, 5%). I've seen that different pH, different concentration in ethanol and detergent each has different results in both...
  9. A

    Square root of negative complex exponential

    Homework Statement Solve \sqrt{-e^{(i2\pi)/3}} Homework Equations The Attempt at a Solution I seem to be missing something simple, as I take: \sqrt{-1} = i then, e^{(1/2)*(i2\pi)/3} which comes out as: ie^{i\pi/3} however, the solution is: -ie^{i\pi/3}, and I can't seem to see where...
  10. C

    Finding Third Root & Values of p & q

    Homework Statement Given that 2 is a repeated root of the equation 2x^3 + px^2 + qx -4 = 0, find the third root and the values of p and q. Homework Equations b^2 - 4ac(?) The Attempt at a Solution Since it said 2 is a root I plugged in 2 as the value of x and rearranged the...
  11. M

    What is the centroid of the given root locus?

    i just want to make sure I'm doing this correctly as there is some discrepancy in my textbook. i know the centroid is equal to (Ʃpoles - Ʃzeros) / (# of poles - # of zeros) the equation i have is s2 + 2s + 8 / s(s2 + 2s + 10) so the zeros are -1 + i√7 and -1 - i√7 and the poles are 0, -1...
  12. D

    Complex constant from single root.

    Homework Statement Do not use a calculator for this problem. Express your answers using square roots and/or fractional multiples of x. Determine the complex constant c such that v is a root of: z6 - c = 0 Homework Equations v = \sqrt{3} - j The Attempt at a Solution I believe...
  13. D

    MHB Exploring a Dimensionless ODE and its Double Root

    dimensionless ODE $\displaystyle\frac{du}{dt}=ru\left(1-\frac{u}{q}\right)-\frac{u^2}{1+u^2}$ $\displaystyle U=r-\frac{ru}{q}$ and $\displaystyle V=\frac{u}{1+u^2}$ Show using conditions of a double root that the steady state is given parametrically by $\displaystyle...
  14. I

    What is the Limit of the nth Root of a Fraction as n Approaches Infinity?

    Homework Statement Show \lim\limits_{n\to\infty}\sqrt[n]{\frac{1}{n^2}}=1 Homework Equations The Attempt at a Solution No ideas
  15. F

    Factoring a Nasty Equation: Double Root

    r,q are constants. I need to factor this equation such that there is a double root. -\frac{r}{q}u^3+ru^2-\left(\frac{r}{q}+1\right)u+r=0 Are there any tricks for this because this just a nasty equation. I don't know if that is a wise approach but: (au+b)(cu+d)^2 =...
  16. N

    The Dirac delta in squere root of the absolute value

    Dear Forum Users, I have got more math question rather then the physics question. Does someone know if: \mid d(x)\mid^2 equals just d(x), here d(x) is just the Dirac delta ? best regards, nykon
  17. S

    Can Polynomials be Factored if Numerical Approximations to Roots are Used?

    I need to factor x5 - 1.I know (x-1) is a factor and have gotten: (x-1)(x4+x3+x2+x +1) I'm not sure where to go from here. Thanks in Advance.
  18. A

    How to Calculate Cube Root Of 24 digit number?

    Hello Friends, I have a question of calculating a cube root of large number like 24 digit number. I calculated by means of Wolfram but I want to try it myself on paper. Is there a method such as Calculus or Algebraic to find the cube root? Thank you. P.S. I want to use the method for...
  19. S

    How to Simplify a Square Root with Multiple Radicands

    Homework Statement Simplify \sqrt {10 + \sqrt{24} + \sqrt{40}+\sqrt{60}} Homework Equations \sqrt{a+b+2\sqrt{ab}} = \sqrt{a}+\sqrt{b} The Attempt at a Solution \sqrt {10 + \sqrt{24} + \sqrt{40}+\sqrt{60}} = \sqrt {10 + 2 \sqrt{6} + 2 \sqrt{10}+ 2 \sqrt{15}} Stuck...
  20. A

    Proving N-th Root of Unity: e^{\frac{2k\pi i}{n}}

    Homework Statement Prove that z=e^{\frac{2k\pi i}{n}},n\in\mathbb{N},k\in\mathbb{Z}, 0\leq k\leq n-1 is an n-th root of unity. The Attempt at a Solution So I know I have to come to the conclusion that z^{n}=1. I'm thinking of using the property e^{i\theta}=cos\theta+isin\theta, but...
  21. S

    Problem involving square / square root of a complex number

    Homework Statement z = (n + i)^{2} n is a positive real number, and arg(z) = \frac{\pi}{3} Find the value of n. The attempt at a solution I am reviewing old problem sets from years past, and came across this problem that appears pretty simple. I have my old answer as n=\sqrt{3}...
  22. D

    Scientific notation root powers exponents question

    Homework Statement scientific notation I have a problem that displays the 4th root of the square root of 5.2 x 10 to the -9th power Homework Equations 4 . .... ... ... -9 ... sq rt of 5.2 X 10 4 -9 sq rt of 5.2 X 10 The Attempt at a Solution The answer I...
  23. W

    Why there is no answer when negative value is being square root?

    why there is no answer when negative value is being square root? e.g: square root of -9 when i try to find answer from calculator, ''math error '' appears.. so is there an explanation for this question?? this question may looks so weird..but i m juz asking out of curiousity..
  24. B

    Integral of square root - Conflicting solutions

    Can a kind person explain to me why I appear to have two conflicting solutions to: \int^{\frac{1}{\sqrt{2}}}_0dx\sqrt{1-x^2} Solution 1 : Standard trigonometric substitution: x=\sin\theta Integral becomes...
  25. 5

    The Limit of a Root of a Function is the Root of that Limit (delta-epsilon)

    Homework Statement Prove: If \lim_{x \rightarrow a} f \left( x \right) = l , then, if \sqrt[n]{f \left( x \right)} exists, \lim_{x \rightarrow a} \sqrt[n]{f \left( x \right)} = \sqrt[n]{l} . Homework Equations Nothing really... The Attempt at a Solution Okay, so here goes...
  26. A

    What is the difference between roots and weights in Lie algebra theory?

    I need some help with understanding the basics of Lie algebra theory. I suspect my problems are due to a fundamental misunderstanding somewhere so apologies in advance for the naivety of the questions and for the restatement of elementary mathematics. As I understand it elements of Lie groups...
  27. M

    Proving f(x) has one real root

    The problem asked to prove by contradiction that the function has only one real root. They used Roll'es theorem and proved that f ' (x) =/= 0 then they concluded that because f ' (x) =/= 0 then by contradiction the function can have atleast one real root... Look at the picture it has the...
  28. T

    Separating variables within square root expressions

    Please see attached. This is a general question for a more complex thermo problem, but it fits this form. Are there any tricks to getting expressions out of square roots in solving DEs? y=y(x) x=x(t) I want to get y by itself so I can integrate with respect to x, but it is trapped in a...
  29. A

    Mathematica Take a matrix square root in Mathematica

    How in the world do you take the square root of a matrix in Mathematica? All the ways I've tried haven't worked... Thanks!
  30. P

    What is the root source of Light ?

    What is the root source of "Light"? I'm not talking about converted/transformed energy via external sources, i.e. Electricity or heat transformed to Light. Whats the root source? Energy itself?
  31. F

    Does Solving x - √2 = 0 Imply x = ±√2?

    Homework Statement What I am confused about is: x - \sqrt{2}=0 x=\sqrt{2} is it equal to x=\pm\sqrt{2} ? Homework Equations The Attempt at a Solution The way I know it, those two are not equal. But my teacher insists on saying that whenever there is a square root, we should always...
  32. S

    Prove that f(x)=x^4 - x - 1 has exactly one root

    Homework Statement I am trying to prove that f(x)=x^{4}-x-1 has exactly one root on [1,2]. Homework Equations The Attempt at a Solution Step one, by intermediate value theorem I proved that there is at least one root on [1,2]. But I don't know how to go about proving there is...
  33. T

    Complex Analysis: brach of the square root

    Homework Statement Let f be a quadratic polynomial function of z with two different roots z_1 and z_2. Given that a branch z of the square root of f exists in a domain D, demonstrate that neither z_1 nor z_2 can belong to D. If f had a double root, would the analogous statement be true?Homework...
  34. S

    Finding the square root of a matrix

    Homework Statement Let A be the matrix: -5 -3 18 10 Find an invertible matrix X so that XAX-1 is diagonal. Use this to find a square root of the matrix A. Homework Equations DetA - xI (A-\lambdaI)v = 0 The Attempt at a Solution So, I found DetA- xI, which...
  35. I

    How Can Modified Convergence Criteria Enhance Regula Falsi Method Efficiency?

    Using ΔX=XH-XL as one of the convergence criteria in regula falsi may lead to infinite looping, e.g. f(x)=0.5x-2ln(x), with a bracket [7,10]. A better choice is to use the approximation error ΔX=|ΔXR|, i.e, the difference between the current estimate and the previous estimate of the root...
  36. E

    Rudin 1.21 Problem understanding proof of unique positive root to the

    Firstly, the set E is defined: "Let E be the set of all positive real numbers t such that tn<x." Later on the proof goes: "Assume yn>x. Put k=yn-x / nyn-1. Then 0 < k <y. If t ≥ y - k, we conclude that yn-tn ≤ yn-(y-k)n < knyn-1 = yn-x. Thus tn>x, and t is not a member of E. It follows...
  37. Seydlitz

    Integration Method for Irrational Root?

    Homework Statement I need to evaluate this particular integral and I'm confused on what method to use. I'm currently learning integration calculus and I tried doing some introduction on electromagnetic field. Quite unexpectedly the integral turned to be heavy. \int_{-a}^a...
  38. A

    Root Finding Exercise - Finding Value for Equivalent Areas

    How to find value in root finding exercise? I am designing a fountain for a Vegas hotel which sprays water in the shape of a hyperbola onto a screen. The hyperbolas shape is a function of several different variables. I am looking for conditions which will cause the area cast by the bottom and...
  39. Z

    Question about taking the difference between two square root expression

    In Ramakrishna's paper, http://arxiv.org/ftp/arxiv/papers/1111/1111.1922.pdf , he derived equation (9), page 5. It is a difference of two square-roots using an approximation method. Can anyone help in how this is done? Thanks
  40. V

    What is minimum value of |a+bw+cw^2|? whrere w is cube root of unity?

    a,b,c are integers not all equal and w is the cube root of unity then minimum value of |a+bw+cw2|(w is not equals one). My answer |a+bw+cw2|<=|a|+|bw|+|cw2| |a|+|bw|+|cw2|=a+b+c. so at lest one value of |a+bw+cw2| will smaller than the minimum value of a+b+c. for integers this minimum...
  41. J

    Convergence: Root Test Inconclusive

    Homework Statement I'm this series to see if it's convergent or divergent. I tried the root test, but it came out inclusive, and now I am trying to figure out if the ration test works. The only thing I'm asking which would be the right test for this. Homework Equations ∞Ʃn=1...
  42. R

    Proving no primitive root mod mn, where m&n prime

    Homework Statement if m, n are distinct odd primes, show that the set of units mod mn has no primitive root. Homework Equations [ hint: phi(mn) = (m-1)(n-1) so we can show for a, a unit mod mn, a((m-1)(n-1))/2 = 1 ] and a \equiv b mod mn iff a\equiv b mod m and a \equiv b mod nThe Attempt at...
  43. S

    Expressing a root of a cubic polynomial as a series

    Is there a good way to do this? I have an equation, say x^3 - 4*x^2 + 2, so a=1, b=-4, c=0, d=2. Is there an easy way to express the largest root of such an equation? In this case, the roots are: 3.8661982625090223 -0.65544238154983 0.7892441190408067 But I am trying to find an...
  44. N

    Root Locus Sketching: Learn How to Draw and Analyze

    Hello, I do not understand very well how to sketch a root locus plot. I am able to find poles/zeros, where the root locus exist on the real axis, the break away/in points, intersection of asymptotes, crossing of the imaginary axis, etc., but I do not understand how to actually draw the root...
  45. W

    Intermediate Value Theorem and Rolle's Theorem to show root

    Homework Statement Use the Intermediate Value Theorem and Rolle's Theorem to show that f(x) = 2x-2-cosx has exactly one root. Homework Equations The Attempt at a Solution I'm not really sure what the question is asking for. the theorems I believe are to prove the existence of a...
  46. R

    "Principal Branch Square Root of z in Domain C-{0}

    Homework Statement Does the principal branch square root of z have a Laurent series expansion in the domain C-{0}? The Attempt at a Solution Well I'm not really sure what a principal branch is? I believe that there is a Laurent series expansion for z^(1/2) in C-{0} because originally our...
  47. C

    Solving Square Root Equation: Step-by-Step Guide to Finding Theta

    Homework Statement Hello. I'm trying to solve this equation: 16.9038=\sqrt{1470tan\theta} Homework Equations The Attempt at a Solution I just need to know what theta is. It's been a while since I've calculated something like this and just need someone to show me the steps...
  48. C

    Differentiation problem square root function

    I'm on mobile so I can't use latex. Differentiate: g(x)=√(4-x^4) , x is a set of [-√2, √2] and determine the domains. So I got the derivative which is, g'(x)=(-4x^3) ^1/2 What should I do with the -+√2 ? I don't know what to do next
  49. Twinflower

    Deriving a root and a fraction

    Homework Statement Derive y= \sqrt(2x^4) - \frac{5}{3x^2} The Attempt at a Solution I am still at the first part of the function (the root): First I tried to derive inside the root like this: \sqrt(2x^4) = \sqrt(8x^3) = 2 \sqrt(2) \times \sqrt(x^3) = \sqrt(2) \times x^2...
  50. 1

    Newtons Method and Finding the 5th root

    Homework Statement Find the 5th root of 36 accurate to four decimal places Homework Equations xn+1 = xn - f(xn)/f'(xn) The Attempt at a Solution First I attempted to write the fifth root of 36 in exponential form as show below: Let the 5th root of 36 = x Let f(x) =...
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