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. R

    MHB Are rationals adjoin cube root of 3 a field?

    Is \mathbb{Q}(\sqrt[3]{3})=\{a+b\sqrt[3]{3}+c\sqrt[3]{9}\mid a,b,c\in\mathbb{Q}\} a ring? If it is a ring, is it a field? I have shown that it is a ring; however, I am not sure that it is a field, since in my calculations it does not seem to be closed under inverses. But I read somewhere that...
  2. johann1301

    Proving √2 Irrational - Explanation & Solution

    Homework Statement In this task we will show that √2 is irrational. Assume that √2 = a/b where both a and b are natural numbers. Let a = p1p2p3...pn, and b = q1q2q3...qm be the prime factors a) explain why 2q1q1q2q2q3q3...qmqm = p1p1p2p2p3p3...pnpn √2=a/b b√2=a...
  3. Jay1

    MHB Computing The Arbitrary-Precision Nth Root Of Positive (X) In PHP

    PHP has some powerful arbitrary-precision (BC or binary calculator) arithmetic functions which seem to be greatly underused and only consist of the basic arithmetic operations, a square root function, a mod function and an integer power function. However, those basic operations can be used to...
  4. anemone

    MHB Prove that a root of an equation is in the interval (1,1+1/k)

    Show that for every integer $k\ge 2$, the equation $x^k+\dfrac{1}{x^k}=1+x$ has a root in the interval $\left(1, 1+\dfrac{1}{k} \right)$.
  5. M

    Finding the Limit of a Root Test: Calculating the Limit of a Challenging Term

    Hello. How do I find the limit of this term? $$\lim_{{n}\to{\infty}}|\left(\frac{n}{n+1}\right)^{\!{n^2}}|^\frac{1}{n}$$ This is the working but I don't understand how to get the third line. r = lim(n→∞) |[n/(n+1)]^(n^2)|^(1/n) ..= lim(n→∞) [n/(n+1)]^n ..= lim(n→∞) 1 / [(n+1)/n]^n...
  6. A

    MHB What is the limit of this expression as n approaches infinity?

    Hello. How do I find the limit of this term? $$\lim_{{n}\to{\infty}}|\left(\frac{n}{n+1}\right)^{\!{n^2}}|^\frac{1}{n}$$
  7. A

    MHB Which Test Should I Use: Ratio Test or Root Test in Series Convergence?

    Hello. How do I determine whether to use ratio test or root test in determining whether a series is convergent or divergant? For example, in this problem, ratio is used for no.1 and root test for no.2. Why is that? I need explanation, please.
  8. M

    Which Test to Use: Ratio or Root? Understanding the Convergence of Series

    Hello. How do I determine whether to use ratio test or root test in determining whether a series is convergent or divergant? For example, in this problem, ratio is used for no.1 and root test for no.2. Why is that? I need explanation, please.
  9. A

    My proof that the square root of 2 multiplied by r is irrational

    Here it is, for you to critique. This is a proof by contradiction. This is a good example of how I usually go about doing proofs, so if you give me tips on how to improve this particular proof, I'll be able to improve all my other proofs. I just learned how to do proof by contradiction...
  10. 9

    Need digital root calculation for large numbers

    for about first 429407636 pi digits where can i get such software or how can i calculate it? (i have 1b pi digits)
  11. A

    Using Newton Raphson for Root Finding and Parameters' Estimation

    Goood Day, I have a cubic root equation. I use Newton-raphson for finding the roots. I want to do parameter estimation (tuning of the equation parameters to be able to give better prediction) using experiment data. Can anyone help me on how to do this? Thanks for your anticipated help...
  12. J

    Integral with infinitesimal under root

    I want compute the following integral: $$\\ \int f(x,y) \sqrt{dx^2+dy^2}$$ Is correct this pass-by-pass: $$\\ \sqrt{\left( \int f(x,y) \right)^2} \sqrt{dx^2+dy^2} = \sqrt{\left( \int f(x,y) \right)^2 (dx^2+dy^2)} = \sqrt{\left( \int f(x,y) \right)^2 dx^2 + \left( \int f(x,y) \right)^2 dy^2}...
  13. T

    Vector & Square Root Question for GCSE Maths

    I have attached a copy of a vector question which i cannot do, i do not even understand what the question is asking can someone help? On a different note i seem to have a lot of trouble with simplifying square roots for example what is the square root of 2704/ is there any way to find the...
  14. K

    Root Locus - Why it is not possible to locate poles arbitrarilly?

    The root locus design method is used to locate poles at desired locations. However, it is not possible to locate poles arbitrarily. Provide reasons for this statement. K = 1/│G(s)H(s)│ K G(s)H(s) = (2k+1)π I've formulated the answer for this as, The root locus gives the path of...
  15. I

    MHB If c > 1, prove that its n^th root is greater than 1 too

    HelloI am trying to prove that if $c > 1$, then $c^{1/n} > 1$ , where $n\in \mathbb{N}$. Now I present my proof here. Since $c>1$, it follows that $c > 0$. Now $n^{\mbox{th}}$ root theorem says that if $a>0$,then there exists a unique positive $n^{\mbox{th}}$ root of $a$. So $c^{1/n} > 0 $...
  16. Saitama

    MHB Cube root of unity with a huge exponent

    Problem: Let $y=x/(1+x)$, where $$\Large x=\omega^{2009^{2009^{\cdots \text{upto 2009 times}}}}$$ and $\omega$ is a complex root of 1. Then $y$ is A)$\omega$ B)$-\omega$ C)$\omega^2$ D)$-\omega^2$ Attempt: I somehow need to show that the huge exponent is of the form $3k$, $3k+1$ or $3k-1$...
  17. J

    How can I evaluate f(x) based on Theorem 3?

    Homework Statement In F17, 2 is a primitive 8th root of unity. Evaluate f(x) = 7x3+8x2+3x+5 at the eight powers of 2 in F17. Verify that the method requires at most 16 multiplications in F17. Homework Equations You can can more clearly see the theorem on page 376-378 and the problem is on page...
  18. S

    Binomial series - Finding square root of number problem

    Homework Statement Expand ##(1+x)^(1/3)## in ascending powers of x as far as the term ##x^3##, simplifying the terms as much as possible. By substituting 0.08 for x in your result, obtain an approximate value of the cube root of 5, giving your answer to four places of decimals. Homework...
  19. mesa

    Question about nth root of unity

    Homework Statement Determine the nth roots of unity by aid of the Argand diagram...Homework Equations Is the nth root of unity where we have a complex number to the 'nth' power equal to 1? For example, $$(2+i)^n=1$$ The Attempt at a Solution None yet, still trying to translate the question.
  20. J

    Is x equal to the 4th root of y in the equation y=x^4?

    If ##y=x^4##, so x is equal to ##\pm \sqrt[4]{y}## or x is equal to ##\pm \sqrt[2]{\pm \sqrt[2]{y}}## ? Well, I think that x is qual to ##\pm \sqrt[4]{y}## because ## \\y=x^4 \\\sqrt[4]{y} = \sqrt[4]{x^4} = \sqrt[2]{\sqrt[2]{(x^2)^2}} = \sqrt[2]{|x^2|} = \sqrt[2]{|x|^2} = ||x|| = |x| \\ \pm...
  21. 1

    Square root of a Mersenne Number is irrational

    Homework Statement A user on math.se wanted to prove that any Mersenne number m = 2^n - 1 has an irrational square root for n > 1. So, it can be proved rather easily that any non-perfect square has an irrational root, and that all of the numbers to be considered are not perfect squares...
  22. Albert1

    MHB Manipulation of square root function

    $\dfrac {\sqrt {3-3x}+\sqrt {x+6}}{\sqrt {1-4x}+\sqrt {2x+8}}=\dfrac {\sqrt {3-3x}-\sqrt {x+6}}{\sqrt {1-4x}-\sqrt {2x+8}}$ please find :$x$
  23. P

    Raising to half power = PRINCIPAL square root?

    This may seem like a very elementary question...but here goes anyway. When a positive number is raised to the power 1/2, I have always assumed that this is defined as the PRINCIPAL (positive) square root, e.g. 7^{1/2} = \sqrt{7},. That is, it does not include both the positive and negative...
  24. maistral

    Cubic EoS - only VAPOR root is converging o_o

    Hello. I would like to inquire as to how to deal with the said topic title. I'm trying to generate a VLE graph for ethylene oxide-water. While I know that EO will quickly vaporize since the boiling point of EO is quite low, I'm still trying to generate a VLE using SRK. So while the vapor...
  25. A

    Are There Closed Form Approximations for nth Order Polynomial Roots?

    Do there exist closed form approximating expressions for the roots of an nth order polynomial?
  26. anemone

    MHB Find the largest positive real root

    Find the largest positive real solution to the equation $7x\sqrt{x+1}-3=2x^2+3x$.
  27. X

    Control Systems - Root Locus with proportional control

    Homework Statement Homework Equations See below The Attempt at a Solution Root Locus? Easy Peasy right? Based on provided equation G(s), i solved the coordinates of the root locus diagram using quadratic equation. For the 2nd part of the question, i have to find gain at which rise time...
  28. N

    Integral involving square root and exp

    Homework Statement \int\frac{dx}{\sqrt{e^{x} + 1}} Homework Equations Using u-substitution The Attempt at a Solution Let u = \sqrt{e^{x} + 1} \Rightarrow u^{2} - 1 = e^{x} Then, du = \frac{e^{x} dx}{2\sqrt{e^{x} + 1}} \Rightarrow dx = \frac{2u du}{u^{2}-1} So...
  29. M

    What is the Constructibility of the Square Root of 2?

    Sorry for any mispellings, English is not my first language. So, I'm studying irrational numbers and I got curious about something and my teacher couldn't give me the answer. I understand Pi must exist because it's the simple result of a division (perimeter by diameter). But how can the...
  30. W

    Indefinite trigonometric integral with an Nth Root

    Homework Statement Solve: \int sin(16x) \sqrt[a]{cos(16x)}\,dx Answer should be linear in the constant "a" The Attempt at a Solution \int sin(16x) \sqrt[a]{cos(16x)}\,dx Set: u=cos(16x), du=-16sin(16x) du ~~\Rightarrow~~ {-1/16}\int \sqrt[a]{u}\,du =...
  31. S

    Algebra and square root simplification

    Homework Statement Points A and B are 10 km apart and it is determined from the sound of an explosion heard at those points at different times that the location of the explosion is 6 km closer to A than B. Show that the location of the explosion is restricted to a particular curve and find...
  32. A

    MHB How to Integrate (x^2 + 2x + 1)sqrt(4x^2 + 8x + 5)?

    how do i integrate (x^2 + 2x + 1)sqrt(4x^2 + 8x + 5)??
  33. C

    Show that r is repeated root for characteristic equation iff

    Homework Statement A:B→B a linear operator Show r is multiple root for minimal polynomial u(x) iff >$$\{0\}\subset \ker(A - rI) \subset \ker(A - rI)^2$$ note: it is proper subsetHomework Equations The Attempt at a Solution Homework Statement My thought: I know ker(A−rI) is basically {{0}...
  34. F

    Complex Square Root Analyticity

    Homework Statement Let f(z) denote the multivalued function (z^{2} − 1)^{1/2} . Define a branch of f(z) which is analytic in the interior of the unit disk |z| < 1 2. The attempt at a solution Having a bit of trouble getting started. I have rewritten f(z) as ((z-1)(z+1))^{1/2} as...
  35. S

    Root Mean Square Speed Units Question

    Homework Statement "At 273 K and 1.00x10^-2 atm, the density of a gas is 1.24x10^-5 g/cm^3. A.) Find the Vrms for the gas molecules B.) Find the molar mass and identify the gas (Choose from H2, He, H20, N2, O2, or CO2)" Homework Equations Vrms = √(3RT/Mm) pV = nRT The Attempt...
  36. C

    Is There More Than One Solution for Cube Root Equations?

    Lets say I was trying to figure out the restrictions of a radical equation and the function inside the radical was a cubic function. I know you have to make the equation inside greater than or equal to 0. In the case of a quadratic equation, you have to square root it once you bring everything...
  37. J

    Complex number polynomial, with no root given

    Homework Statement z^3 + (-5+2i)z^2 + (11-5i)z -10+2i =0 has a real root, find all the solutions to this equation. The Attempt at a Solution I have only solved imaginary number polynomials with a given root, but this has no given root, how do I find the real solution? that I can then...
  38. C

    Proof that the Square Root of 2 is Irrational.

    I am trying to prove that √2 is irrational using proof by contradiction. Here is my work so far: √2 = p/q where p & q are in their lowest terms. Where q is non-zero. 2=p2/q2 2q2 = p2 Which tells me that p2 is an even number, using the definition of an even number. We can use this definition...
  39. J

    Calculating the root mean square speed from pressure and density.

    Homework Statement A tyre contains gas at a pressure of 150 kPa. If the gas has a density of 2.0 kg m-3, find the root mean square speed of the molecules. Homework Equations These are the equations I believe to be relevant: c_{rms} = \frac{\sqrt{<c^2>}}{N} pV = \frac{1}{3}Nm<c^2> p =...
  40. anemone

    MHB Compute a square root of a sum of two numbers

    Compute $\sqrt{2000(2007)(2008)(2015)+784}$ without the help of calculator.
  41. I

    Integrating a Square Root Function: Solution

    Homework Statement ∫(0,1) √x/√[3]1-x Homework Equations \Gammap\Gammaq/\Gammap+q The Attempt at a Solution p-1=1/2 →p=3/2 q-1=-1/3 →q=2/3 β(3/2,2/3)=\Gamma(3/2) \Gamma(2/3)/\Gamma(13/6) \Gamma3/2=1/2\Gamma(1/2)=√π/2 \Gamma2/3=-1/3 \Gamma13/6=7/6 1/6=7/36 β(3/2,2/3)=-6√π/7
  42. kini.Amith

    What is the Value of √i + √-i?

    Homework Statement The value of √i + √-i , where i=√-1 is (a) 0 (b) 1/√2 (c) √2 (d) -√2 Only one option can be chosen Homework Equations The Attempt at a Solution Let (x + iy)2=i Solving for x and y, I got √i = +1/√2 (1+i) or -1/√2...
  43. A

    Finding the power series of a square root

    Homework Statement Find a power series for f(x) = \frac{1}{\sqrt{4+x^{2}}}, at x=0. 2. The attempt at a solution I have looked up the Taylor series of \frac{1}{\sqrt{4+x^{2}}}, but I don't find any similarity with a power serie like \sum_{n\geq 0} a_{n} x^{n} I don't know how to start...
  44. T

    Find the root of integral equation

    Homework Statement Hi everyone. I have encountered a weird equation while doing some research and I have no idea how to solve it. The equation goes like this ∫ dR / (1+ c*r) ^ (a/r) = d, limits of integration are from 0 to Rmax, where Rmax ^2 = [u]^2 - α^2, where u is a constant value...
  45. A

    Defining the square root of an unbounded linear operator

    I have started coming across square roots (H+kI)^{\frac 12} of slight modifications of Schrodinger operators H on L^2(\mathbb R^d); that is, operators that look like this: H = -\Delta + V(x), where \Delta is the d-dimensional Laplacian and V corresponds to multiplication by some function. But...
  46. R

    Medical Root Canals & Cancer: Is There Evidence?

    I recently had a friend on facebook share this website Edit by mentor: link deleted it suggests there's a causal relationship between root canals and cancer. Right off the bat, given the website name, realfarmacy, i was skeptical. I tried to check their sources and did a few searches on google...
  47. N

    What Temperature Triples the RMS Speed of an Ideal Gas?

    Homework Statement An ideal gas has rms speed vrms at a temperature of 288K . At what temperature is the rms speed tripled? Homework Equations P=(NmV2)/3V The Attempt at a Solution I'm kind of stumped on this one. Other ones I've done are pretty simple to figure out, but the...
  48. S

    Root Mean Squared: Solving for n in Homework Equation

    Homework Statement Attached Homework Equations Attached The Attempt at a Solution in my equation for Vrms I am confused to as what values I use for "n" and what "n" stands for in the equation. any help would be greatly appreciated! thanks pf
  49. W

    Sketching Root Locus of System: K Varies 0 to ∞

    Hello guys, I need help to sketch the root locus of the system when K is varying from 0 to infinity. (K>=0) The system: http://www.freeimagehosting.net/newuploads/anspe.jpg I'm stuck. I really don't know how proceed. Thanks in advance.
  50. H

    What is the limit of a function under a square root?

    Homework Statement lim x-> 2+ f(x)=sqrt(4-x^2)whats the value of the following function?? Homework Equations The Attempt at a Solution i tried and got the answer as does not exist but some people got it as 0 which is the correct answer
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