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. hamad12a

    How to find the third root of z^3=1?

    Homework Statement in a given activity: solve for z in C the equation: z^3=1 Homework Equations prove that the roots are 1, i, and i^2 The Attempt at a Solution using z^3-1=0 <=> Z^3-1^3 == a^3-b^3=(a-b)(a^2+2ab+b^2) it's clear the solution are 1 and i^2=-1 but i didn't find "i" as a solution...
  2. S

    B Proof that non-integer root of an integer is irrational

    I have been looking at various proofs of this statement, for example Proof 1 on this page : http://www.cut-the-knot.org/proofs/sq_root.shtml I'd like to know if the following can be considered as a valid and rigorous proof: Given ##y \in \mathbb{Z}##, we are looking for integers m and n ##\in...
  3. S

    Interval of Convergence of Power Series with Square Root

    I'm trying to find the answer to a question similar to this posted it earlier but in the wrong section I think and not explained well. $$ \sum_{{\rm n}=0}^\infty \left (-\sqrt x \right )^n \ \ \rm ?$$ Find the interval of convergence? I tried using the root test and got from 0 to 1 but when I...
  4. S

    I Square Root in an alternating power series

    I had a question similar to Σ0∞ (-1)^n (x)^(n/2) and attempted to solve it using the root test getting abs(√x)<1, but I've also seen some places answer it as √abs(x)<1 so am I skipping a step.
  5. anemone

    MHB Cos (π/7) is a root to a cubic equation

    Prove that $\cos \dfrac{\pi}{7}$ is a root of the equation $8x^3-4x^2-4x+1=0$.
  6. kaliprasad

    MHB Showing the Other Root of $4x^2+2x-1= 0$ Given $\alpha$

    If one root of $4x^2+2x-1= 0 $ be $\alpha$ then show that other root is $4\alpha^3-3\alpha$
  7. Alpharup

    I Root of nth Degree Polynomial f(x) in Spivak Calculus Ch. 7

    In chapter 7 of Spivak calculus, it is proved that if n is odd, then the 'n'th degree polynomial equation f(x) has a root. I do understand what goes into the proof and can follow steps easily. But, my question is 1.How did they think of a proof like that? 2.By trial and error, did they find...
  8. P

    Root Mean Square: What It Is & Why It Matters in Electrical Engineering

    What is the root mean squad (RMS) of a signal (or wave) and why is it important for electrical engineering? How do you Find it? What is it used for? Thank You All
  9. M

    MHB Principle Ideal in F[x] & Primitive nth root of unity

    Let ζ5 be e2πi/5. Find a monic polynomial of degree two in K(ζ + ζ−1) So, if E/F is a field extension, with α∈E then K(α) = {f(x)∈F[x] | f(α)=0} and m(x) is the minimal polynomial of α over F such that K(α) = [m(x)] where [m(x)] is the ideal generated by m(x). I was thinking maybe (x- ζ -...
  10. alexmahone

    MHB What Does the Branch of the Cube Root Function Mean?

    Let $f(z)=z^{1/3}$ be the branch of the cube root whose domain of definition is given by $0<\theta<2\pi$, $z\neq 0$ (i.e. the branch cut is along the ray $\theta=0$.) Find $f(-i)$. Could someone please help me understand the question? I'm not too clear on "branches" and "branch cuts".
  11. L

    Square Root Simplified: Understanding the Result as a Single Nonnegative Number

    How is it equal to v in the end? I'm sorry for asking such questions. But I'm just trying to understand
  12. L

    Can someone give me a hand with large root here

    i get the differentiation the halves cancel the 2 the h bar cancels the h bar square and to get rid of the root in the denominator the entire thing is squared But I cannot understand where the huge square root came from at the end where I circled. Can someone help me here
  13. anemone

    MHB Can You Prove $a > \sqrt[9]{8}$ is a Root of a Polynomial with $1 < a < 2$?

    Let $1\lt a \lt 2$, $a$ is a root of the equation $x^5-x-2=0$. Prove that $\large a>\sqrt[9]{8}$.
  14. RJLiberator

    [Abstract Algebra] Field and Polynomial Root problem

    Homework Statement Suppose a field F has n elements and F=(a_1,a_2,...,a_n). Show that the polynomial w(x)=(x-a_1)(x-a_2)...(x-a_n)+1_F has no roots in F, where 1_f denotes the multiplicative identity in F. Homework EquationsThe Attempt at a Solution Strategy: We have this polynomial...
  15. wolram

    What is the root cause of cancer

    One reads of cancer ever more these days, it seems like one can get cancer of anything, surly there must be a different switch to switch on breast cancer or prostate cancer.
  16. S

    MHB Quartic polynomial has at least one real root

    Hello, Given the quartic: $$16x^4-40ax^3+(15a^2+24b)x^2-18abx+3b^2 = 0$$ where $a,b$ are certain real constants. My question is if there is a (simple) condition on $a$ and/or $b$ such that the quartic has at least one real root. Since the quartic has real coefficients the only possibilities...
  17. RJLiberator

    Comp Sci Solve C++ & ROOT Problems: 3 Questions Answered

    I have three problems that I've been trying to tackle for a while now. 1) I have a code for the bisection method. I would like to use TLine *line = new TLine function to create the lines that you normally see in the bisection method. These lines from a to F(a) are the ones I am talking...
  18. Mr Davis 97

    Pulling a negative out of a square root

    The following is invalid, since the operation is not defined when ##a, b < 0##: ##\sqrt{-1}\sqrt{-1} = \sqrt{(-1)(-1)} = \sqrt{(-1)^2} = \sqrt{1} = 1##. This is not correct, because ##ii = -1##. This shows that ##\sqrt{a}\sqrt{b} = \sqrt{ab}## is invalid when ##a, b< 0##. However, say we have...
  19. M

    Calculator (root) problem (Exam tomorrow) HP 10s assistance

    Homework Statement Hello, I have to use the HP 10s calculator at my university, I have been used to my modern casio for the last 4 years but I have a problem. The square root symbol when pressed does not allow for continual calculation, such as when I am using the quadratic formula. It seems to...
  20. A

    Calculating Square Root of a Matrix in Quantum Information Theory

    I'm doing an online course in quantum information theory, but it seems to require some knowledge of linear algebra that I don't have. A definition that popped up today was the definition of the absolute value of a matrix as: lAl = √(A*A) , where * denotes conjugate transpose. Now for a...
  21. RJLiberator

    Comp Sci C++ (ROOT) Form a matrix and send it to a 2d Histogram

    Homework Statement [/B] 1. I've been tasked with forming a 10 x 10 matrix with elements 0, 1, 2, 3, 4, 5,... and have it display properly. 2. Then, take this matrix and make a 2d-histogram out of it. Homework Equations Here is my code void matrix6( const int n = 10) { float I[n][n]; //...
  22. Z

    MHB Is My Root Test Solution Correct?

    Hey, I am working on this problem over the root test but I am not sure if I am doing it right. I will attach my work to this thread and I really want someone to look over my work and see if I am doing it right. By the way I didn't finish the problem because I was not sure where to go from my...
  23. RJLiberator

    How Can I Optimize My ROOT Code for Array Initialization and Graphing?

    Homework Statement The goal is to create two arrays that have the values a = { 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 } b = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} And then graph them so that a=mb slope m thus being 2. I am working on the first part before I graph them. Homework EquationsThe Attempt...
  24. RJLiberator

    Advice: Software: ROOT and course: Applied PDE

    Tomorrow I embark on a new semester and this semester I have the pleasure of learning applied partial differential equations and the software of "ROOT" ROOT: https://root.cern.ch/ So I am here to solicite advice. 1. In regards to ROOT, is there anything that can set me up better for a more...
  25. E

    Simplifying square root of an irrational

    Homework Statement Find [(3 - 51/2)/2]1/2 Homework EquationsThe Attempt at a Solution My calculator says (-1 + √5)/2 I have no idea how. Rationalising doesn't really do much good. Just tell me where to start.
  26. anemone

    MHB Is $10^a\lt 127$ True for the Real Root of $x^3-3x-3=0$?

    Given $a$ is the real root for $x^3-3x-3=0$, prove that $10^a\lt 127$.
  27. anemone

    MHB Cube Root Challenge: Prove Inequality

    Prove $\sqrt[3]{43}<\sqrt[3]{9}+\sqrt[3]{3}<\sqrt[3]{44}$
  28. anemone

    MHB Challenge of Square Root Problem

    Show that $\sqrt{99}-\sqrt{98}+\sqrt{97}-\sqrt{96}+\cdots-\sqrt{4}+\sqrt{3}-\sqrt{2}+\sqrt{1}> 5$.
  29. B

    Definition of Principal Square Root?

    Is the principle square root just the positive and negative roots of any number (as opposed to just the positive)? I've seen some confusing definitions of this term online and thought I'd double-check with knowledgeable math people here. Lastly, if it is just the + and - roots of any number...
  30. R

    Double root of equation with Newton Raphson

    Homework Statement Find a double root of the equation ## f(x)= x^3+15.87x+24.34 ## correct to 3 decimal places. Homework Equations By Newton Raphson's Formula, ## x_{n+1}=x_n + \frac{f(x_n)}{f'(x_n)} ## ##f'(x)=3x^2+15.87 ## The Attempt at a Solution Does a double root means to find two roots...
  31. terryds

    How Do You Rationalize the Denominator to Solve for a+b?

    Homework Statement If ##\sqrt{\frac{10+4\sqrt{6}}{10-4\sqrt{6}}}=a+b\sqrt{6}##, then a+b is ? A) 8 B) 7 C) 6 D) 5 E) 4 The Attempt at a Solution [/B] This is my attempt...
  32. ChrisVer

    Root histograms in multi-files

    Suppose I have a collection of 40 directories, each containing 1, 2 ,3 ,4 or 5 .root files with histograms and trees. What is an optimal way to merge those .root files so I would end up with 40 directories and 40 root files with the histos added together? One way I thought of was to start typing...
  33. A

    Integrating a square root function

    Problem statement: Find the arc length of the curve defined by x = √t and y = 3t -1 on the interval 0 < t < 1attempted solution: dx/dt = 1/2t-1/2 , dy/dt = 3 and dx = dt/ 2√t dy/dx = 6√t length = ∫01 √(1 + (6√t)2) .dt/ 2√t = ∫01 √1 + 36t) dt/2√t now I'm stuck with a product that is very...
  34. A

    Integrating a polynomial with a square root

    1. Integrate the following: (4x - x^2)^1/2 dx 2. Any assistance would be appreciated.3. Honestly don't know where to start.
  35. B

    Understanding the Truth behind 2 ≥ √2

    Why is this true? It is bigger but it is not equal to
  36. chimath35

    Limit problem with square root

    I have done this problem before but forgot how to get from one step to the next: let a>0. how is absval(x^1/2-a^1/2) equal to abval(x-a)/(x^1/2-a^1/2)?
  37. ChrisVer

    How can I use event-wise weights in the TMVA factory?

    I have one question (simple I hope). In the TMVA factory one can set global weights by typing: // global event weights (see below for setting event-wise weights) Double_t signalWeight = 1.0; Double_t backgroundWeight = 1.0; And use them afterwards by calling their names signalWeight...
  38. D

    Square root function: x intercept paradox?

    Here's my equation y= sqrt (x+4)+1 I want to find the x intercept. Ok so i replace y with 0 and solve for x 0= √(x+4)+1 -1=√(×+4) (-1)2=×+4 1=×+4 -3=× So it looks like the x intercept is (-3,0) But then when i go back and plug in -3 in place of x... y=√(-3+4)+1 y=1+1 y=2 I now have a point...
  39. ChrisVer

    What Does ROOT TH1::SetDirectory Do?

    Can someone explain me what SetDirectory actually does? I found the problem with a macro like that: #include<iostream> #include <TH1F.h> #include <TCanvas.h> #include <TFile.h> int histoSum(){ //create histograms to use TH1F* histo1 = new TH1F("histo1",";A", 100, 0,10); TH1F* histo2 = new...
  40. Destroxia

    Is ± Present When Taking 4th Root?

    Homework Statement If you take a 4th root of something, is that answer also plus or minus, just like if you are taking a square root? Ex. ##4^{\frac 1 2} = ±2## So following that logic, would that mean that: ##16^{\frac 1 4} = ±2## as well? Meaning, is the ± still present if you take a 4th...
  41. F

    Regarding root mean square velocity

    I am stuck with this question: why can't we use the equation c(rms)=√(3RT/M) for problems when no of moles is not 1? Because I think the mole will be deduced as c(rms)=√(3nRT/nM) =√(3RT/M) For instance I found this problem, given atmospheric pressure is 10^5 Pa, molecular mass of Nitrogen...
  42. ChrisVer

    How Can I Implement ROOT Multivariate Reweighting in a Program?

    Suppose I have a programme. In there I have the creation of histograms: signal: histo_s_Pt histo_s_v1 histo_s_v2 background: histo_b_Pt, histo_b_v1 histo_b_v2 iteration to fill signal/bckg from events j. So at this point I'm having the 6 above histograms filled. Now if I wanted to compare...
  43. W

    MHB Solve Root of Equation Q1a: Help Here

    Can you help me question 1a?
  44. N

    Integral of exponential over square root

    Hello guys, How can I evaluate the following integral please? ##\int_{-\infty}^{+\infty}\frac{e^{i A x}}{\sqrt{x^2+a^2}}dx## Thank you
  45. epenguin

    Were you taught square root extraction at school?

    And what are the methods? This was stimulated by This question could be rephrased as "use the method for finding square roots you were taught in school to find √7 to 6 decimal places". If you were taught at school. If you were not taught at school you were luckier than me, I was. It has had...
  46. C

    Solving Square Root Problems: 10^2+10^2 to 10*√(2)

    Hi I'm just wondering: How does √(10^2+10^2) become 10*√(2) ? I also noticed that √(10^2+10^2+ 10^2) becomed 10*√(3) But how to you mathematically - ith more steps- go from √(10^2+10^2) to 10*√(2)? Kind regards, Christian
  47. Q

    About cartan and root generators of lie algebra

    I am reading the text Group Theory A Physicist's Survey of Ramond, in particular chapter 7. He explains classical lie algebra structure using cartan generators and root generators. He sometimes uses reality condition of structure constant( i think he supposes that all generators are...
  48. ChrisVer

    What happens when rebinning a histogram with non-divisible number of bins?

    Hi, I am having one histogram that contains 101 bins. I tried rebining it with the TH1::Rebin: histogram->Rebin(2.); But I got the warning message that 2 is not an exact divider of 101. I looked in ROOT TH1 Rebin's page, and read this note: I don't understand what the execution of the...
  49. B

    MHB Finding eigenvectors for a double root

    I have the following matrix: [-1 3 -3(2)^0.5 ; 3 -1 -3(2)^0.5 ; -3(2)^0.5 -3(2)^0.5 2] I was able to find the eigenvalues as -4 and 8. I am now trying to find the corresponding eigenvectors how since -4 is a double root i am unsure how to go about this. I have tried using gaussian...
  50. G

    Square root of complex number on a calculator

    I'm working through some examples in a textbook but i am unable to get the desired answer on my calculator, i keep getting math error and various other results which are not the answer I'm looking for. What i have is: √ 62.9∠88.2 / 0.00165∠72.3 Please could someone tell me what answer you get...
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