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

    How accurate is the square root of a number?

    This may sound like a silly question but: How accurately has the squareroot of numbers like 2,3,5 etc. been measured? When you type it into a calculator it gives you an answer with a certain amount of decimal points, the calculator is of course software programmed by a group of people who can't...
  2. S

    Limit problem simplify the root

    Homework Statement [/B] I feel like I'm missing some theorem which is preventing me from finalizing this problem! It's been driving me nuts I feel like I'm missing something super basic! Ultimately they've given the solution, g/8, so I know this is how I should try to get the equation to look...
  3. X

    MHB Find Positive Square Root of 30

    find the positive square root of 70-20\sqrt{30}
  4. M

    Root and exponent of matrix

    Homework Statement I. 3*3 matrix A (8 2 -2, 2 5 4, -2 4 5) II. 3*3 matrix (1 2 0, -1 -2 0, 3 5 1) Homework Equations I. Solve Aexp 100 of 3*3 II. Find the 5th rooth of B matrix The Attempt at a Solution I. I got stuck at diagonalising the matrix. Is this OK 1st step ? If yes...
  5. A

    Root Locus Question: Unraveling Intuition for Stability Analysis

    Homework Statement I've been trying for a week to understand root locus and how it works but what i got is a big confusion that's why I'm asking here for help. Why do we only look at open loop transfer function of the system when we are supposed to know the stability of the closed loop system...
  6. K

    MHB Find Min Polynomial of $\alpha$ Over $\mathbb{Q} | Solution Included

    I started by setting $\alpha= e^{2\pi i/3} + \sqrt[3]{2}.$ Then I obtained $f(x) = x^9 - 9x^6 - 27x^3 - 27$ has $\alpha$ as a root. How can I proceed to find the minimal polynomial of $\alpha$ over $\mathbb{Q},$ and identify its other roots?
  7. Emmanuel_Euler

    Finding a cube root of a number without using calculator .

    HI EVERYONE I was thinking if we could find a cube root without using a calculator. square root was easy to find without calculator,but cube root i have no idea to find it. any help?? for example(cube root of 3 or 2)
  8. Emmanuel_Euler

    Square Root Rules: x^(1/2), abs(x), F(x), & More!

    hi guys i know all square root and any root(cubic...) rules sqrt(x)=x^(1/2) sqrt(x^2)=abs(x) sqrt(xy)=sqrt(x)*sqrt(y) sqrt(x/y)=sqrt(x)/sqrt(y) sqrt(-x)=isqrt(x) f'(x)=1/2sqrt(x) F(x)=2/3*(x^3/2) ..... my question is: is there any rules for this sqrt(x+y) or sqrd(x-y)?? any help please??
  9. T

    Sketching Root Locus: n=2, m=1, Angle?

    The characteristic equation is 1+K(S+1)/S2 Below is the root locus diagram. I don't get why there are two branches when there is only one pole, at 0. Does it count as having two poles even if it is the same because of s^2 ? If it does then why doesn't the angle of departure make sense? number...
  10. T

    Finding root of complex equation

    Homework Statement Good day, I've been have having difficulties finding the roots of this: Find the roots of 3ix^2 + 6x - i = 0 where i = complex number i = sqrt(-1) Homework Equations quadratic formula (apologies for the large image) The Attempt at a Solution...
  11. B

    Plant root and nitrogen experiment

    Homework Statement A high school experiment shows a plant immersed in a solution of nitrate ions. The beaker is closed but has an air vent passing into the solution. Q. Why is air bubbled into the solution Q. Why is the beaker covered with black paper Homework EquationsThe Attempt at a...
  12. B

    Is the square root of 4 a constant?

    I don't know what to say. sqrt(4) = +/- 2, but constants are fixed. When written sqrt(4), it seems sqrt(4) is a constant, but not in the latter case. Help!
  13. 2

    Finding the nth root of a complex number?

    Homework Statement Find the solutions to z^{\frac{3}{4}}=\sqrt{6}+\sqrt{2}i Homework Equations de Moivre's theorem The Attempt at a Solution z^{\frac{3}{4}}=2\sqrt{2}e^{\frac{\pi i}{6}}=2\sqrt{2}e^{\frac{\pi i}{6}+2k\pi}=2\sqrt{2}e^{\frac{\pi +12k\pi}{6}i} z=4e^{\frac{4}{3}{\frac{\pi...
  14. Rapier

    Root Plotting 2d-Array in Histogram

    Homework Statement The task is to plot a 2-d surface of the potential and field lines calculated from a numerical method. In this case, there is a charged box (v = 1) @ r = 1 (it's not round, but each side is d = 2 and the center of the box is at the origin) and the edges of the box are v=0...
  15. A

    I'm a little rusty, cant solve x+e^x=b

    Homework Statement Hi, I'm new here. I'm really rusty, I resume my career this year, and I'm reading 'the spivak book', (for Calculus 1). Making some exercises, I get curious about how to solve this: x+e^x=4 I would love if someone could give me any trick Homework EquationsThe Attempt at a...
  16. P

    Finding the correct value of k so a root is a factor of P(x)

    Homework Statement P(x)=x^24-2kx^6+k^2 Find all values of k so that (x-(sqrt(3)/2+i/2)) is a factor of P(x) Homework Equations The Attempt at a Solution Letting z=sqrt(3)/2+i/2 mod(z)=1 arg(z)=π/6 z^(24) gives e^(24π/6)i=e^(2πi)=1 z^(6) gives e^(6π/6)i=e^(π)i=-1 If (x-(sqrt(3)/2+i/2)) is...
  17. R

    How to simplyfy a square root term? Phonon dispersion relati

    I'm having trouble simplyfying this, I guess there's a trick but for the life of me can't remember what it is. Here is what I have so far: ##\omega ^{2} = f\left ( \frac{1}{m}+\frac{1}{M} \right )-f(( \frac{1}{m}+\frac{1}{M} \right ))^{2} - \frac{4q^{2} a^{2}}{mM})^{\frac{1}{2}}## so I divide...
  18. T

    Algorithm to find square root of a quadratic residue mod p

    I'm going through an explanation in a number theory book about Tonelli's algorithm to find the square roots of a quadratic residue modulo ##p## where ##p## is prime, i.e. I want to solve ##x^2 \equiv a \pmod{p}## with ##(\frac{a}{p}) = 1##. The book goes as follows: Let ##p - 1 = 2^s t##, where...
  19. I

    Understanding square root of a polynomial

    Hello This is not exactly a homework problem. I was browsing through an old book, "Elementary Algebra for Schools" by Hall and Knight, first published in England in 1885. The book can be found online at https://archive.org/details/elementaryalgeb00kniggoog . I was studying the process of...
  20. S

    Every nonnegative real has an nth root proof

    I need help understanding this proof. The textbooks says, For every k∈{1,...,n} there exists an mk∈ℕ such that (n choose k) rn-k 1/mkk< δ/n His justification for this, is that for every real number x there exists an natural number n such that n≥x. I fail to see the connection between the two...
  21. I

    MHB Growth proportional to square root of worth.

    Hi! :o I'm stuck :confused: I was thinking I need to use the equation $f=kw^2$ but I'm really not sure.
  22. P

    Partial derivative of a square root

    Hi, I'm using partial derivatives to calculate propagation of error. However, a bit rusty on my calculus. I'm trying to figure out the partial derivative with respect to L of the equation: 2pi*sqrt(L/g) (Yep, period of a pendulum). "g" is assumed to have no error. I know I can use the...
  23. ognik

    MHB Newton-Raphson algorithm for the root of tanh

    The N-R (iterative) formula is: xi+1=xi - f(xi) / f '(xi). A textbook exercise states that the N-R method does not converge for an initial guess of x >~ 1. I wrote the required program for tanh and found the method diverges at x >~ 1.0886. But I don't understand why it is this value - the N-R...
  24. Logan Land

    MHB See if series converges using the root test

    ((2+i)/(3-4i))^(2n) I know it converges with 1/5 < 0 but I don't understand how to obtain 1/5 unless somehow its like this (2+i)^2 = (4+1)=5 (3-4i)^2 = (9+19)=25 which is 5/25 which is 1/5 but that doesn't seem like the correct way to me
  25. D

    MHB How to Calculate Cube Root of a Number in 10 Seconds

    The first and the most important step is to memorize the cubes of 1 to 9. These would form an important part of your toolkit in solving the cube roots. Here is a table for your convenience. 1 –> 1 2 –> 8 3 –> 27 4 –> 64 5 –> 125 6 –> 216 7 –> 343 8 –> 512 9 –> 729 Once you memorize this list...
  26. F

    Root Locus Sketching: Why Is -0.435 the Breakaway Point?

    Hi guys. Firstly the answer to the requirement of the post is all in the picture (problem statement, relevant equations etc.). I'm just wondering if someone could tell me why they use the root -0.435 as the breakaway point? Like I know there's two real roots; -0.435 and -1.61, so obviously one...
  27. AdityaDev

    How can \sqrt x and \log_e x be compared using calculus?

    I was going through some important points give in my textbook and I saw this: ##\log_e x < \sqrt x## How did they get this? I know calculus so you can show this using differentiation, etc. One possible way is that they took ##f(x)=\sqrt x-\log_e x## And tried to prove it is always greater than zero.
  28. Berlin

    Square Root of Inverse Metric

    Anyone noticed this paper: Square Root of Inverse Metric: The Geometry Background of Unified Theory? Authors: De-Sheng Li, arXiv:1412.2578 ? The author tries to construct the square root of the inverse metric, based on a product of a fermion field and a framefield. Somehow the Standard model...
  29. P

    How to compute the norm of a root from the Cartan matrix?

    Hello! As far as I understand, the Cartan matrix is associated with a unique semi simple algebra. How can we compute the norm of a root α from it since its components are invariant under rescaling (if all the simple roots are multiplied by the same constant, the Cartan matrix remains unchanged)...
  30. W

    Digital Root: A Strangely Interesting Operation

    Digital root (adding a number's digits together repeatedly until a single digit answer is obtained) doesn't seem like a very interesting operation, but it has some weird properties. One of the first someone might notice is that dr(n) = dr(n+9) This is fairly easy to demonstrate. But after...
  31. anemone

    MHB Find Real Root: $x^5-10x^3+20x-12=0$

    Find a real root of $x^5-10x^3+20x-12=0$.
  32. RJLiberator

    Root Test and Integral Test Question

    Homework Statement [/B] From K=4 to infinity the Σ (-1)^k (k/e^k) Converge or diverge? Use: a) Ratio Test b) Root Test c) Integral Test d) Alternating series test Homework EquationsThe Attempt at a Solution For the alternating series test and ratio test I have the correct answer that it...
  33. L

    Finding the Critical Point(negative square root)

    Homework Statement Find the critical points for the function g(x, y, z) = x3+xy2+x2+y2+3z2. Homework EquationsThe Attempt at a Solution I've come up with the following 3 equations (derivatives set so that they are equal to 0) (1) 3x2+y2+2x=0 (2) 2xy+2y=0 (3) 6z=0 From (3), z=0 From (2)...
  34. M

    Squared numbers and square root (Need help with explaination)

    Can anyone tell me why for example the speed of light is squared in "E=mc^2" ? Also what does square root mean and why is it in certain equations like for example time dilation? What happens if you exclude the square root and the y^x in a equation? I am still studying high school physics, but...
  35. T

    MHB How can you factor out x from the original term?

    In a text, We have this: $\sqrt{2x^2 + 1}$ is equal to $x \sqrt{2 + \frac{1}{x}}$ I am confused as to how to factor out x from the original term.
  36. C

    MHB What is the Square Root Property in Mathematics?

    Dear everyone, I have a question about a property of square root. $${\frac{1}{x}\sqrt{x^2}}$$$\implies$ $\sqrt{\frac{x^2}{x^2}}$=$\left| 1 \right|$ Is that property of a square root? Since $$\sqrt{x^2}$$= $\left| x \right|$.
  37. Albert1

    MHB Find the Solution to $a^2-b^2$ with $a+bi$ a Root of $z(z+i)(z+3i)=2002i$

    $a+bi$ is a root of :$z(z+i)(z+3i)=2002i$ here :$a,b>0$ and $i=\sqrt {-1}$ please find :$a^2-b^2=?$
  38. PcumP_Ravenclaw

    Square root of 2 divided by 0 is rational?

    Dear All, Please help me understand how ## \sqrt{2} ## divide by 0 is rational as stated in the excerpt from alan F beardon's book?
  39. snoopies622

    Expanding Cube Roots: Solving Limits with Maclaurin Series

    A quiz at the end of Steven Krantz's Calculus Demystified includes the following problem: Find \lim_{x \to \infty} [ \sqrt[3]{x+1} - \sqrt[3]{x} ] I see how one can use the Maclaurin series to get \sqrt[3]{x+1} = 1 + \frac {x}{3} - \frac {x^2}{9} + \frac {5 x^3}{81} + . . . but trying it...
  40. F

    MHB Prove that the order of 5 modulo 2^k is 2^(k-2)

    Prove that the order of 5 modulo $2^k$ is $2^{k-2}$ where $k$ is at least 3. I thought probably induction is best bet. For k=3 we can verify. So for inductive step we need to show the order of 5 modulo $2^{k+1}$ is $2^{k-1}.
  41. S

    Finding roots for a root locus

    Hi, In the attached image the roots are shown for the characteristic equation. I don't know how the roots were found. Anyone able to help? Thanks Splint
  42. Z

    MHB How can we simplify this expression involving square roots?

    4\sqrt{n^{2}}+\sqrt{m^{2}n-\sqrt{4n^{2}}}-\sqrt{mn^{2}} I don't even know where to start, I know the teacher said to distribute but distibute what?
  43. O

    MHB Simplifying a square root in a fraction, part of midpoint formula

    I have: sq rt 2 +sq rt 2 over 2 , sq rt 5 + sq rt 5 over 2 I got (sq rt 4 over 2, and 0) = 1, 0 but the answer is actually (sq rt 2, 0) so is my answer still wrong?
  44. iamjon.smith

    Complex Radical or Complex Root?

    solve a radical expression: 1.5r250 (*r denotes the radical symbol) in a radical expression where the index of the root is 1.5 and the number is 250 Use Calculator, Show Steps Homework Equations The Attempt at a Solution First of all, using a calculator the answer comes out to 39.685, but I...
  45. V

    How do I linearize a square root graph?

    Homework Statement These are the Points. X values: 0, 1.98, 3.96, 5.94, 7.92, 9.9 Y values: 1.98, 7.13, 9.08, 11.04, 12.57, 14.51 I need to find the original equation and the linear equation. I can't seem to find the line for square root graphs. 2. The attempt at a solution I know it's a...
  46. T

    MHB Finding domain of a function with square root in bottom of fraction\infty

    I need to find the domain of this function.$$h(x) = 1 / \sqrt[4]{x^2 - 5x}$$ So, I understand that I need to set $$x^2 -5x > 0$$ from that I get $$ x(x-5) > 0$$ and $$ x > 5$$ However, the answer in the textbook is given: $$ ( \infty, 0) \cup (5, \infty)$$ Which mean that the graph has a...
  47. O

    MHB Solving Square Root Questions: A Math Tutorial for Beginners

    How does this work? (Also, I am very math illiterate and do not understand even the most basic terms, if you could kindly speak as you would to a child I would GREATLY appreciate it.) sq rt sign over 13^2 - 12^2 (over both of it together) Now the answer is 5, because (13)(13) - (12)(12)...
  48. teroenza

    Mathmatica Bisection Root Finding

    Homework Statement Write code in Mathematica to find the root of f(x) = \int_0^x \frac{\sin (t)}{t} \, dt-\frac{\pi }{2} using the bisection method. I have attempted to do this using: f[x_] := N[-(Pi/2) + Integrate[Sin[t]/t, {t, 0, x}]] (*Plot[f[x],{x,0,2*Pi}]*) fg =...
  49. E

    Units square root of a Newton

    I have a table with several quantities in it, and one of them is \sqrt{T} (T is tension) I have values for this table, and want to put the units next to the values. Something seems off to me about doing this, I guess because they're not integers. Is it correct to say the units are kg1/2m1/2s-1...
  50. jnbp13

    Easiest Method to Evaluate Imperfect Square Root up to 5 Decimals?

    Easiest Method to Evaluate Imperfect Square Root up to 5 Decimals? Any ideas?
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