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. C

    Integral of an exponential divided by a root function

    Homework Statement Prove that the diagonals of a parallelogram bisect each other. Homework Equations I chose one vertex as the origin, one as a and one as b. The final vertex was a+b. The Attempt at a Solution The diagonals were \vec{r_1}=\vec{a}+\vec{b} and \vec{r_2}=\vec{b}-\vec{a}...
  2. K

    Simplifying Equation With Square Root

    Homework Statement An equation in a book lists this equation: (c - 18)^{2} = (-3\sqrt{c})^{2} And it simplifies it as: c^{2} -45c + 324 = 02. The attempt at a solution When I do out the equation, I get: c^{2} + 324 = 9 + c i squared c, then -18 for the left side of the equation, then for the...
  3. B

    Root Finding of complex trig function

    Homework Statement a) Show that for small values of x, xtanx is approximately equal to x^2 and 2 - coshx is approximately equal to 1 - 0.5(x^2). Draw a conclusion from this regarding the probable number and approximate locations of roots on the interval [-1,1]. b) Use Newton's method to...
  4. S

    Finding the domain of the square root of a polynomial

    I was just going through some problems in a maths journal for undergraduate level i found a sum seeming simple but i am not able to solve it completely find domain of \sqrt{x^{12} - x^9 + x^4 -x +1}i know domain includes all negative value , all positive value >1 , but i can't get anything...
  5. S

    Reducing Sqrt(4t^2+4+1/t^2): Calculus Problem Help

    reducing sqrt(4t^2+4+1/t^2) to (1+2t^2)/t The Attempt at a Solution - This is actually just a portion of a calculus problem, but I can't figure out how the book did the algebra here. I get (2t^2+2t+1)/t and don't know how that reduces to (1+2t^2)/t. Please help.
  6. S

    How do i integrate: square root of((x^2)-4) ?

    how do i integrate: square root of((x^2)-4) i know i have to use substitution but what do i substitute?
  7. B

    What is the meaning of square root cut in Zee's Quantum field theory?

    Hello! I am just working through Zee's Quantum field theory in a nutshell and have a little problem. He calculates the free propagator and evaluates an integral (I doubt the integral is important for my question) when he writes "and the square root cut starting at \pm i*m leads to an...
  8. R

    Integral with sq. root in it again

    Integral with sq. root in it...again Homework Statement Find.. \int x^\frac{3}{2}\sqrt{1+x} dxHomework Equations The Attempt at a Solution Well I used the fact that: \sqrt{1+x}=\sum_{n=0} ^\infty \frac{(-1)^n(2n!)x^n}{(1-2n)(n!)^24^n} and well I just multiplied by x^\frac{3}{2} so I...
  9. Holocene

    Finding the Nth Root of a Number without a Calculator

    Is there any "pencil and paper" method to find the nth root of a number? Since multiplying a number by itself any number of times quickly yeilds extremely large numbers, trial and error might seem to pinpoint the root of a number, so long as it is a perfect square or cube or whatever. But...
  10. A

    Root Test: Convergence of Series

    Homework Statement Determine whether the series converges or diverges. \sum_{n=2}^{\infty}\frac{1}{(\ln n)^{\ln (\ln n)}}=\sum_{n=2}^{\infty}\frac{1}{e^{\ln (\ln n)\ln (\ln n)}} The Attempt at a Solution for u=\ln (\ln n) \sum_{u=\ln (\ln 3)}^{\infty}\frac{1}{e^{u^2}}...
  11. P

    Integral from 1 to infinity of 1 / xln(third root of x)

    Homework Statement Integral from 1 to infinity of 1 / xln(third root of x) 2. Homework Equations n/a 3. The Attempt at a Solution I tried to find if it diverged and then got lost after that Homework Equations The Attempt at a Solution
  12. T

    Zero vs. Root: Exploring the Differences

    What's the difference between a zero and a root? cheers.
  13. R

    Prove that if m, n are natural, then the root

    Hi, I've encountered this exercise which I'm having a hard time proving. It goes like this: Prove that if m and n are natural, then the nth root of m is either integer or irrational. Any help would be greatly appreciated. Thanks.
  14. W

    Finding a Cubic Root: Pencil and Paper Technique

    I still remember how to extract a square root without a computer but could somebody remind me the technique to find a cubic root just with the pencil and paper?
  15. C

    Complex Roots: Solving for the Number and Identification

    Homework Statement State the number of complex roots and then identify what the roots are. Equation: 18x^2 + 3x -1 = 0 Homework Equations The Attempt at a Solution There are 2 complex roots. Okay. So I can't factor anything out of the equation and when you try to factor it...
  16. A

    Different results in the unit root test. Why?

    Situation: I had tired a 1000-data generated by random error(i.i.d.), then I sub it into different unit root tests. I got different results among the tests. The following are the test statistics I got: For R project: adf.test @ tseries ~ -10.2214 (lag = 9) ur.df @ urca ~ -21.8978 ur.sp @...
  17. L

    Root Loci of Double Integrator: PI & PD Controllers

    Homework Statement For the double integrator described with transfer function G(s) = \frac{1}{s^2} the initial condition is zero. The double integrator is subjected to a unit‐feedback system where the controller is chosen as 1) a PI-controller with C(s) = k_p \left( 1 + \frac{1}{s}...
  18. B

    Finding a monic polynomial with 2^.5 + 3^.5 as a root

    Homework Statement Number Theory homework. I'm supposed to prove that the value 2^.5 + 3^.5 is irrational by finding a monic polynomial that the aforementioned number is a root of. This would be trivial if I were supposed to prove that just 2^.5 was irrational because its monic polynomial...
  19. M

    Integration with a square root

    Homework Statement The problem is really about finding the length of a parametrically defined curve, this in itself seems easy enough, but it's the integration part that's hard. The problem is as follows: x = cost y = t + sint t = 0...pi The Attempt at a Solution So in order to...
  20. A

    Can All Coefficients 'a' and 'b' Be Roots in Their Own Set of Quadratics?

    1. Homework Statement : We have 'n' quadratics is the form x^2 +aix+bi All values of A and b are different. Is it possible to have all values of A and B as the roots of the n quadratics 2. The attempt at a solution: Well. I know that all values of 'a' and 'b' must (if possible) be in one...
  21. T

    FIRST: Highest & Lowest Root of f(x) = x^2 - 2x + 1

    FIRST What is the HIGHEST root? If there is a highest root, are there available any LOWEST root? Say, what is the highest and lowest root of f(x) = x^2 - 2x + 1? SECOND What happen if I sum the EVEN and ODD function? I don’t think I am a good on geometry. THIRD What is the integral of...
  22. T

    Proving that cube root 7 is irrational

    Hi guys, How would you prove that \sqrt[3]{7} is irrational without using the unique factorization thrm? I tried proving that \sqrt[3]{7} is rational but it didn't seem to get me anywhere... Thanks EDIT: Looks like I posted this in the wrong forum.
  23. M

    A complex complex root

    G'' = -kG k is a constant solving this ODE, r = +/- sqrt(-k) if k > 0, then r = +/- sqrt(k)i so G is in the form Acos(sqrt(k)x) + Bsin(sqrt(k)x) so, what if k is a complex number, then r = +/- sqrt(-ki) then what is the form of G?
  24. S

    What is the limit of the sequence (Xn) = (n!)^(1/n)?

    I'm working on the limit of the sequence (Xn) = (n!)^(1/n) Pretty sure it diverges as n goes to infinity, but unsure how to show it. Any hint would ge greatly appreciated.
  25. C

    R= the square root of x^2 + y^2

    Homework Statement This problem is #17 in Chapter 3 of Giancoli's 5th Edition Physics. The summit of a mountain, 2085 m above base camp, is measured on a map to be 4580 m horizontally from the camp in a direction 32.4 degrees west of north, What are the x, y, and z components of the...
  26. B

    Integration of a composite square root function, easy (hard for me )

    Integration of a composite square root function, easy (hard for me :( ) Homework Statement How would I integrate: y = \sqrt{(1 + 4x^2)} Homework Equations - The Attempt at a Solution I have no idea how to do this. I tried to to the chain rule in reverse, and then I ignored it, but I can't...
  27. R

    How to integrate a function with a square root in it

    Homework Statement find \int x^{\frac{3}{2}}\sqrt{1+x} dx Homework Equations The Attempt at a Solution Now i tried all the methods i know of which include integration by parts and substitution,the integration by parts didn't work too well, so substitution I tried. let...
  28. V

    Is the root mean square current always positive?

    Am sorry, if this topic does not belong to this section, as i am new, kindly oblige Can root RMS value of current (what we study in Alternating currents) be negative? i feel that it can surely be negative as it is a root, but my teacher told that it can't be negative and showed just one...
  29. W

    Calculating Eigenvalues: 0 Root Meanings

    This is just a general question: If, when you are calculating the eigenvalues for a matrix, you get a root of 0 (eg. x^3 - x) --> x(x-1)(x+1), what does that mean for the eigenvectors? thanks, w.
  30. J

    One integral (square root and gaussian peak)

    An integral \int\limits_{-\infty}^{\infty} \sqrt{1+x^2} e^{-Ax^2+Bx} dx is the problem. Anyone knowing the solution?
  31. M

    Find a Polynomial Function of Degree 5 with Roots: 2, √7, 5i, and -5i

    Homework Statement Find a Polynomial function of degree 5 whose zeros are: 2, radical 7, and 5i Homework Equations Multiplying rootsThe Attempt at a Solution Hello, well it's my first time at these forums so just following the template given. Thanks for any help by the way I'm just so...
  32. L

    Square Root Graph: Understanding x- & y- Intercepts

    I'm confused on the graph: y=\sqrt{x}-4 I know the x- and y-intercepts which are: (0,-4) and (16,0) but I don't know if the graph extends to the negative x (3rd Quad). You can never square root a negative number and get a real number right? Therefore, does the graph just stop at the...
  33. marcus

    Expanding Space: the Root of all Evil?

    thoughtful paper on how to convey an idea with least confusion http://arxiv.org/abs/0707.0380 Expanding Space: the Root of all Evil? Matthew J. Francis, Luke A. Barnes, J. Berian James, Geraint F. Lewis 8 pages, accepted for publication in PASA (Submitted on 3 Jul 2007) "While it remains...
  34. K

    What is the Argument of a Complex Number with a Given Modulus?

    z^4= 1/2 + i sqrt(3)/2 I start by transforming into polar form: z^4 = e^(i*Pi/3) But then I'm blank.
  35. Ahmed Abdullah

    Is root over a^2=modolus of a?

    Is "root over a^2=modolus of a?" mod of a is always positive, but root over a^2 can both be positive or negative. So how these two can be equal to each other? I have found this in a math textbook. But I can't convince myself about it. It will be very helpful if you give a proof. Thnx in...
  36. A

    Math Mystery: Why Is \sqrt{2}^{4} Not 4?

    Isn't \sqrt{2}^{4} equal to 4?? How come when I plug this into my calculator it gives me the number:3.999999999996 , which is very close to 4 but isn't?? Is there something wrong with the settings of my calculator?
  37. T

    Root of n degree of the number n

    Root of "n" degree of the number "n" Hello! Frankly speaking I am not sure whether this is proper forum, because I am not sure if this exercise involves calculus or not... The task is: Consider the numbers "root of "n" of n degree", n >= 2. How many of them are equal? Justify your answer...
  38. Ahmed Abdullah

    What are the differences between a root and a rhizome?

    Mosses and ferns have rhizome whereas a mango tree has root. Rhizomes are used for absorbing water and nutrient from ground by mosses as higher plants use their roots. SO I don't understand why two distinct terms are used for things of similliar functions.
  39. Y

    Square root of a rotation matrix

    I am having a hard time figuring this out. Suppose we have a 4x4 matrix A, B and rotation matrix D. Matrix A represent position and orinetation of object1, matrix B represent position and orientation of object2. Matrix D is the position and oreintation of object2 relative to object1. B = D*A...
  40. W

    How is square root calculated?

    Just bored and decided I want to make my own little calculator on my computer. What is the method for finding the square root of an input number?
  41. N

    Asymptotic behaviour of a polynomial root

    I've been looking at the value N(n) of N that satisfies the equation \sum_{1}^{n}(N-i)^{n}=N^{n} Thus turns out to be N(n)=1.5+\frac{n}{ln2}+O(1/n) where the O(1/n) term is about 1/400n for n>10. I've verified this by calculation up to about n=1000, using Lenstra's long...
  42. W

    Mastering Square Roots: Simplifying Division, Addition, and Subtraction

    I feel embarassed to ask these questions but what is the rule for to simplify division, addition, and subtraction square roots? Here are some questions: SIMPLIFY:5\sqrt{24}\div2\sqrt{18} \sqrt{40} + \sqrt{90} \sqrt{50} - \sqrt{18}
  43. L

    Applications of Integral Calculus to Root Solving

    As a Grade 12 student that is often required to find the roots of quadratics for math, physics, and chemistry problems, I wondered whether there would be any methods for solving these problems excepting the quadratic formula. I was pondering the implications of calculus in algebra and, although...
  44. N

    What is the Root of i? A Surprising Discovery for a 3rd Year Physics Student

    I am a 3rd Physics student and this is news to me! apparently root of i is exp(iPi/2))^1/2 Why? Of course by i I mean Root of minus 1
  45. D

    Derivation with x^2 and root x

    Homework Statement derivate: x^2 \sqrt{x} Homework Equations (u \cdot v)^\prime = u^\prime \cdot v + v^\prime \cdot u The Attempt at a Solution I found: (x^2)^\prime = 2x (\sqrt{x})^\prime = \frac{1}{2 \sqrt{x}} I entered them into the equation: 2x \cdot \sqrt{x} + x^2...
  46. S

    Using root test and ratio test for divergence

    Homework Statement Does this series converge or diverge? Series from n=1 to infinity n(-3)^(n+1) / 4^(n-1) Homework Equations The Attempt at a Solution Okay, I've tried it both ways. Ratio test: lim n --> inf. ((n+1)*(-3)^(n+1)/4^n) / (n * (-3)^n / 4^(n-1)) Now...
  47. V

    Yes or no, Can you square root a zero

    Yes or no, Can you square root a zero. This is for a limits question.
  48. A

    How can the integral of the square root of t squared plus 9 be evaluated?

    Homework Statement \int \sqrt{t^2+9} Homework Equations The Attempt at a Solution Apparently you can't solve this equation as you would \int \sqrt{t+9}, which would come out to \frac{2(t+9)^3/2 }{3}. Instead, my calculator is getting this extremely complicated answer involving ln functions...
  49. V

    The root numbers in toothpaste (help)

    Pardon me for not using latex. Homework Statement A toothpaste box has square ends. The length is 12cm greater than the width. The volume of the box is 135cm^3. What are the dimensions of the box? Homework Equations Quadratic theory, Random pluggin for x, common factoring, Family of...
  50. G

    Square Root in Special Relativity

    Can anyone explain what the square root does? I know 3 squared equals the square root of 9. I want to learn what is actually happening behind the math, if that makes sense. Consider the following: I’m calculating the wavelength of light, and traveling towards the source. Speed of light =...
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