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. E

    Is it possible to take the ith root of some number?

    And if so, could I take the ith root of i?
  2. H

    How to solve recurrence relation with one real root and two complex roots ?

    How to solve recurrence relation with one real root and two complex roots ? The Example is ; Solve the recurrence relation a n-1 + a n-3 = 0 where n ≥ 3 and a 1 = 1 a 2 = 1 a 3 = 2 a n = nth order a n-1 = (n-1)th order. a n-3 = (n-3)th order. I've started the solving ; a n = r^n so...
  3. A

    Is the Square Root of 2 Rational?

    sorry, I am using phone, owho i hope you can get it. suppose its rational. in the form a/b gcd(a,b)=1 and so and so and so and then they concluded that a^2=2 is a contradiction. but i cannot see what it conradict the assumption. help
  4. L

    Changing the y axis range in a TH1F in root

    hi, I am plotting a 1D graph in root (TH1F pointer). currently the y-axis gives the number of entries in each bin along my x-axis. how do i change it so that it is actually the number of entries in each bin divided by the total number of entries. thanks
  5. B

    Calculating a Square Root Without Calculator

    Hi all, I am trying to find a nice back-of-the-envelope way to numerically-calculate nasty things like square roots and stuff. For instance: \sqrt {4.51} = ? I tried to use a linearization: \sqrt x = \sqrt {n + \varepsilon } = \sqrt {\left[ {{\rm{integer}}} \right] + \left[ {{\rm{decimal...
  6. D

    Integration by substitution where square root is U^2

    Hi there, I am having difficulty with one aspect of intergration by substitution where the substituion of a square root is U^2, wondering if anyone can help. Problem: Integral of: 2x√(3x-4) dx by substituting U^2 = 3x-4 Would du^2/dx = 3 therefore 1/3 du^2 = dx (I think...
  7. O

    The square root of a 2x2 matrix

    Given a symmetric 2x2 matrix, what would be the way to calculate the square root of it? Here, http://www.jstor.org/stable/2689616?seq=2 , it is announced that a relatively simple formula could be applied for the resulting matrix entries, but I could not access it further. Thanks
  8. Telemachus

    Integral containing something over the root of x²-a²

    Homework Statement Evaluate the next integrals, expressing it previously in the forms that contains \sqrt[ ]{a^2+u^2}, \sqrt[ ]{a^2-u^2} and \sqrt[ ]{u^2-a^2}, and then solve it using the integral table; The exercise which I couldn't solve...
  9. K

    Meaning of the square root and its contradiction

    Is square root a function in this way? f:\mathbb C\rightarrow\mathbb R^+ However contradiction can be drawn:\sqrt{x^2}=|x|\text{ and } i^2=-1 \sqrt{-1}=\sqrt{i^2}=|i|=1 \sqrt{-1}=1 ??What is the problem in the...
  10. A

    Differential Equation Root of Pt (aka xy)

    Homework Statement dP/dt=root of (Pt) Homework Equations P(1)=2 The Attempt at a Solution Well, I figure that the integrating factor is 1, since there is no P(x) value, so it's a matter of finding the integral of root(Pt). I can't solve this because the only method I know is...
  11. S

    Calculating Square Root of 144400 Using Taylor Series | Understanding Calculus

    1. square root of 144400 using Taylor series 2. I used the equation of sqrt(x) for x>2 given in http://www.understandingcalculus.com/chapters/23/23-1.php 3. I have tried it upto the 7th power and I got sqrt(144400)=1/0.209482810=4.773661 I know sqrt(144400)=380; and...
  12. H

    Finding the fourth root of 6.0 x 10

    Homework Statement If Kp = 6.0 x 108 For equilibrium N2 <--> 2N Then what is the equilibrium constant of N <--> .5N2Homework Equations K= C^c/A^aThe Attempt at a Solution I tried finding the fourth root of 6.0 x 108 and that didn't give the right result. BTW the answer is 4.1 x 103, I'm...
  13. M

    What is the proof for minimizing the sum of distances on a sliced rectangle?

    Homework Statement Hi guys, I'm doing a rather long math modelling task. As part of the task, I have to investigate the following argument: There is a rectangle ABCD. It is sliced by the line EF, such that EF is parallel to AD and BC. M is the midpoint of BC. X is a point on the line...
  14. G

    Finding Open Loop Transfer Functions and Critical Stability in Root Loci

    Hi, I ve got two problems. 1) The problem i have is how to find an open loop transfer function that gives poles at -3, -6, -7+_ j5 and zero at -5. So i think that the numerator is (s+5), and denominator has (s+3),(s+6). and now I don't know how to carry on. Is it ( s+7+j5) and (s+7-j5)?. Am I...
  15. U

    GF(q); x^p-x+a has no root => irreducible [PROOF]

    Homework Statement Let q=p^e, where p is a prime and e is a positive integer. Let a be in GF(q). Show that f(x)=x^p-x+a is irreducible over GF(q) if and only if f(x) has no root in GF(q) Homework Equations The Attempt at a Solution One of the directions seems obvious. Namely, if...
  16. U

    Char(F)=p; poly NOT irreduc. => must have a root?

    Homework Statement Let F have prime characteristic p and let a be in F. Show that the polynomial f(x)=x^p-a either splits or is irreducible in F[x]. I was given a hit: "what can you say about all of the roots of f in a splitting field?"Homework Equations The Attempt at a Solution Suppose f...
  17. A

    SImpe question about square root function

    Is it a right mathematical operation (a*b)^0.5 = a^0.5 *b^0.5 when a and b either both are negative or one of them is negative.
  18. R

    What is this mathematical trickery? (removing a square root?)

    Homework Statement So I was doing the following relativity problem: An atomic clock moves at 1 000 km/hr for 1 hr as measured by an identical clock on the Earth. At the end of the 1 hr interval, how many nanoseconds slow will the moving clock be compare with the Earth clock? The problem...
  19. N

    Units of Square root of a quantity

    Homework Statement Example: If the tension in a string is 25N, the square root of that tension would be 5 ...what?
  20. srfriggen

    Root Test, Infinite Series

    Homework Statement I don't have the problem in front of me but it was something like "converge or diverge"?: \sum 5^n/(n+1) The Attempt at a Solution I would like to know that if I use the root test, would I get lim n-> \infty 5/(n+1)^1/n = 5/(n+1)^0 = 5/1 = 5 ? I suspect...
  21. D

    Finding general soln of differential eqn (zero under the root)

    Homework Statement 9y'' + 6y' + y = 0 r^2 + 6r + 1 ( -6 +/- root 36 - 36 ) / 18 lamda = -6/18 = -(2/9) mu = 0 (this is the part I am unsure about, because if i end up with a zero under the root, then does this make the final equation into this: y = c_1*cos(0*x) +...
  22. C

    Converting square root to perfect square

    Homework Statement Hi, I have a problem in my book in which they use a method of making sqrt( 36 + x^2 ) a perfect square by simply making x = 3( t - 1/t ) and then we get 9( t + 1/t )^2 by substituting back into sqrt(36 + x^2). My question is that why did the chose 3( t - 1/t ), is...
  23. R

    Newton-Raphson & Bisection Methods to Find x2- 2 Root

    Homework Statement Using the Newton raphson method with x0=6, find the root of x2- 2 to 3dp. Then estimate the number of iterations the bisection method that would be required to achieve the same accuracy. Homework Equations The Attempt at a Solution I have done the first...
  24. r-soy

    Find six distanct sixth roots of -1 + i root 3 I want check my answer

    Find six distanct sixth roots of -1 + i root 3 I want check my answer ==== > x = -1 y = root 3 r = 2 tan Q = 2pi/3 -1 + i roo3 = 2 { cos ( 2 pi / 3 ) + i sin 2 pi / 3 ) = 2 e ^2 pi i / 3 } now six root -1 + i roo3 = 2^1/6 e ( 2 pi/3...
  25. S

    Show that sq. root of 2 to power sq. root of 2 to N converges

    Show that sq. root of 2 to power sq. root of 2 to ... N converges Sq. root of 2^sq root of 2 ^ sq. of 2...N Use monotonous convergence theorem to that it converges and determine what it converges to.
  26. C

    Find the square root of: 4+4(sqrt3)i

    Homework Statement find the square root of: 4+4(sqrt3)i put the answer in a+bi form Homework Equations finding the nth roots: √(r(cos(theta)+isin(theta)))=√r(cos(theta+2(pi)(k)/(n))+isin(theta+2(pi)(k)/(n) where k=0,1 The Attempt at a Solution first i converted my...
  27. K

    Root Mean Square Error, a straight line fit and a gradient issue

    I have some measurements from a physics lab experiment and I am coding in Matlab a fit for the data. [Note this is not a problem with Matlab, my problem here is theory] In normal regression of statistics the RMSE is given by: s=\frac{\sigma}{\sqrt{n}} =\sqrt{\frac{\Sigma (\epsilon...
  28. M

    Understanding the Square Root Loop and Its Construction on S^1 and RP^1

    My notes claim that the square root loop \sigma : S^1 \longrightarrow RP^1 ; z=\cos 2\pi t +i\sin 2\pi t \longrightarrow [\cos \pi t, \sin \pi t] is a homeomorphism, where [x,y] is an equivalence class given by the antipodal equivalence relation on the circle. However, this map doesn't even...
  29. M

    Using the root test find whether the series converges or diverges

    Using the root test find whether the series converges or diverges: Lim Sin (4/(3n+3)) / Sin (4/(3n)) n-> inf. I have no idea how to cancel out the sin terms
  30. G

    Proof Two Primitive Root Conditions Are Equivalent

    Homework Statement Let n be a nonzero integer and let a be an integer with gcd(a, n) = 1. We have two equivalent conditions which characterize primitive roots: (i) a is primitive modulo n if the order of a is \phi(n). (ii) a is primitive modulo n if for every element b with gcd(b, n) = 1 we...
  31. L

    Square Root 3/2 and 0.8660: Explained

    Question is pretty simple : How do I know that square root 3/2 = 0.8660 or how can 0.8660 be converted into square root 3/2 more importantly. My calculator is out of style so it displays only numbers. Thanks
  32. R

    Calculating the Square Root of a Self-Adjoint Positive Definite Matrix

    Homework Statement The matrix C is self-adjoint and positive definite on \mathbb{ C}^2. Determine \sqrt{\mathbb{C}} \in \mathbb{ C}^{2x2} . C=\left(\begin{array}{cc}5&-4i\\4i&5\end{array}\right) The Attempt at a Solution Characteristic polynomial: (5-\lambda)^2 - 16 = 0 What I...
  33. Z

    Convergence or Divergence of Series with Square Roots

    Homework Statement Determine whether the series converges or diverges. \sum (\sqrt {k} - \sqrt {k - 1})^k Homework Equations The Attempt at a Solution (a_k)^\frac{1}{k} = \sqrt{k} - \sqrt{k - 1} What do I do here..? = \frac{1}{\sqrt{k} + \sqrt{k-1}} \to 0 ?
  34. K

    Prove square root of 3 is irrational

    I have no idea how to go about this, except that we are supposed to use proof by contradiction to show that the square root of 3 is an irrational number. Any help or tips is appreciated. Thanks.
  35. S

    Solving for a variable when the square root of a formula is in the denominator

    Homework Statement solve for x: [ x / sqrt(x^2 + h^2) ] = [ d / sqrt(d^2 + h^2) ] I need to solve for x. Homework Equations sq rt * sq rt = what is inside the square root square both sides of an equation The Attempt at a Solution Can anyone help me remember how to get...
  36. T

    Simple roots of a Lie Group from the full root system

    Hello all, I'm attempting to find in literature a method of determining from a Lie algebra's full root system in an arbitrary basis which roots are simple. It seems there are many books, articles, etc on getting all the roots from the simple roots but none that go the other way. My task is...
  37. H

    Square root involving complex number

    I've struggled for days reading about square roots of complex numbers and I get most of the problems but not this one. I really want to understand what is going on in this problem, hope someone can help! 1. The complex number (C) is C = 1/\sqrt{i*x} . find the two roots of C. The solution...
  38. H

    Maclaurin series for square root (1+x)

    Homework Statement Maclaurin series for square root (1+x) Homework Equations The Attempt at a Solution I attempted to find the maclaurin series for the function Square root of 1+x. F(0)=1 first term= 1 F'(0)=1/2 second term= (1/2)x F''(0)=-1/4 Third term (-1/4)x^2...
  39. N

    How to Determine the Sign of the Square Root in ODEs for Photon Orbits?

    hi there, I'm trying to plot r against \phi by solving the following ODEs using runge-kutta. The problem I'm having is with the square root. How do I know when it will be positive and when it will be negative? If this is a simple question I apologise I'm not that great with the maths :). E and...
  40. K

    Can we still use the ratio test if the sequence of ratios diverges to infinity?

    Let ∑ak be a series with positive terms. Ratio test: Suppose ak+1/ak -> c. If c<1, then ∑ak converges. If c>1, then ∑ak diverges. If c=1, the test is inconclusive. What if ak+1/ak diverges (i.e. ak+1/ak->∞)? Do we count this as falling into the case c>1? Can we say whether ∑ak converges...
  41. Mentallic

    Weird Graph Behaviour - Analyzing a Root in Domain 2-4

    I came across this weird graph from another thread: y=\left(x^2-6x+8+\sqrt{x^4-12x^3+52x^2-96x+64}\right)^2 It seems that there is a root y=0 for the domain x=[2,4]. I've never seen such weird behaviour on a graph before. How could analysis of this function (or not?) determine that there...
  42. P

    Integrating the Inverse Exponential-Square Root Function

    Homework Statement \int dx/(e^{x}\sqrt{1-e^{-2x}}) Homework Equations The Attempt at a Solution I have absolutely no idea of how to start the problem, any help is greatly appreciated! thanks!
  43. T

    Square Root of 4: Can it be +2 or -2?

    Consider square root of 4. Can square root of 4 be +2 or -2? I asked that to my math teacher so he said: NO, square root of 4 is +2! But I can't really understand why it cannot be -2 since -2 squared is also 4. One thing I've imagined is: square root of 4 can be +2 or -2, but for...
  44. E

    Root of equation with 2 exponentials

    Homework Statement This isn't really a homework question, but I was considering a different model of library fines... where the fine at the end of the 1st late day is $0.01, and it increases geometrically with a common ratio of 2, so it goes like $0.01, $0.03, $0.07, $0.15... Then I...
  45. I

    Help with sum of infinite series using the root test.

    Homework Statement Does it converge or diverge? Sum n=0 to infinity : (n/(n+1))^(n^2) The attempt at a solution I know I need to use the root test. But what I get is ... Limit to infinity : (n/(n+1))^n It seems that the n/(n+1) would go to 1 because when you multiply the top...
  46. T

    Applications of math - Root finding

    Hello, I came across the following formula after asking for practical applications of math in finance and other sciences, it concerns mortgage payments A = Pi/1-(1+i)^-n The above denominator end part reads (1+i)^(-n) As a mathematical question, is it possible to rearrange the...
  47. M

    C/C++ Fixing a C++ Program Error: Negative Square Root

    hi there, i have written a small program in C++ and if the user puts in the wrong values for some of the variables the operation will end up trying to square root a negative number and this returns that the answer is not a number can anyone show me how to write an if function that if...
  48. S

    Square Root Problem: Equal Expressions?

    1. Homework Statement [/b] i have this thing: 2u\sqrt{}um is this expression the same as: 2u^3/2*m^1/2 Homework Equations The Attempt at a Solution
  49. S

    Linerization of square root of sin(2x)

    Homework Statement Find the linerization of square root of sin(2x) Homework Equations The Attempt at a Solution I don't even know how to start. What is linearization? Thanks
  50. O

    Cubed root denominator limit question

    Homework Statement Evaluate lim x->8 (x-8)/(cubed root of x) -2) Homework Equations The Attempt at a Solution I multiplied both numerator and denominator by (cubed root of x) +2. In the denominator, I wrote it as ((x^1/3)-2)*((x^1/3)+2) which simplifies to (x^2/3)-4. I have...
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