Root Definition and 944 Threads

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. D

    When should the plus/minus sign be used when dealing with square roots?

    Ok, I know this question sounds incredibly elementary, but please don't just dismiss it, try to understand what I'm REALLY asking. Ok, say we have x^{2} = 9. I know the answer is x = \pm 3. But I was just thinking about the general rule to this. I was thinking that what really happens is...
  2. F

    How Do You Integrate 1/(x^(1/2) - x^(1/3))?

    Homework Statement \int\frac{dx}{x^{1/2}-x^{1/3}} Homework Equations None The Attempt at a Solution What I did was replace \int\frac{dx}{x^{1/2}-x^{1/3}} with \int\frac{dx}{u^{3}-u^{2}} if u=x^{1/6}. Just to simplify things. And I think that was pointless. Help me out?
  3. D

    Calculating Pressure and Velocity in a Cylinder of Argon: Tips and Tricks

    Root Mean Square Speed... HELP! A 11.0 cm-diameter, 24.0 cm-long cylinder contains 1.80×1022 atoms of argon at a temperature of 52.0 C. What is (Vx)rms, the rms value of the x-component of velocity? What is the rate at which atoms collide with one end of the cylinder? Determine the pressure in...
  4. C

    Integrating the square root of a linear function.

    Homework Statement \int\sqrt{2*x-1} Homework Equations The Attempt at a Solution Homework Statement Obviously this can be fixed with the antiderivative of a linear function with proper constants i.e. \int A\times f(bx + c) = \frac{A}{b} F(bx + c), however my instructor provided...
  5. M

    Is \sqrt[3]{2} Irrational and Cannot be Represented by Rational Numbers?

    Hey guys. I forget where I found this problem but it goes as follows: Prove that \sqrt[3]{2} cannot be represented in the form p+q\sqrt{r} where p,q, and r are rational numbers. It is easy to show that \sqrt[3]{2} is irrational, so it cannot be put in the form m/n, where m and n are...
  6. W

    How Do You Calculate Cube Roots of Complex Numbers in Modulus Argument Form?

    can someone help me solve this question as fasd as possible?? im really headache wif it... thx~~ determine the 3 cube roots of 3-i over 3+i giving the result in modulus argument form,express the principal root in the form a+Jb
  7. D

    How do I find the square root of 3 - 2\sqrt 2?

    Homework Statement Find the square root of 3 - 2\sqrt 2. Homework Equations The Attempt at a Solution I don't really know how to do this quickly. Could this be done by solving x^2 = 3 - 2\sqrt 2? Or should I solve (a + b)^2 = 3 - 2\sqrt 2? By the way, the answer is 1 - \sqrt 2.
  8. T

    I cant understand the meaning of this root

    http://i42.tinypic.com/2yju26p.gif i know that the root supposed to be a distance but i can't see the distance from where to where?? the charges are not a single point i don't know how they calculate this distance ??
  9. A

    Designing a Cruise Control System Controller with Root Locus Method | Coursework

    Homework Statement I have to design a controller for "Cruise Control System" using Root Locus method. Homework Equations We havnt studied that method yet and nor do I think it is in the course outline. Actually that is why I selected root locus so that I can learn something beyond the...
  10. S

    About the epidermial cell of the root hair.

    Anyone one here, knows any link where there will be a diagram of the epidermal cell of the root hair cell? If not, could you please explain to me everything about the epidermal cell of the root hair.
  11. V

    Efficient Methods for Finding Square Roots without a Calculator

    This has been bothering me for a while now. Without a calculator and without using "guess and check" how can find the square root of a number? For example: 6^{2} = 36 but how can you reverse it and figure out what \sqrt{36} equals? Is there some equation to it or can it only be done using guess...
  12. A

    Standard deviation of root mean square error

    I am comparing two RMS error time-series and I would like to generate error bars on the RMS results. I think the RMS error is a standard deviation of an assumed zero mean process, and I have the gut feeling that this should be the standard deviation of the sample standard deviation. Is that...
  13. B

    Laurent expansion of principal root

    How do I find the Laurent expansion of a function containing the principal branch cut of the nth root? Example: f(z)=-iz\cdot\sqrt[4]{1-\frac{1}{z^{4}}}
  14. K

    What Is the Root of Number Operator in Quantum Mechanics?

    I seen in some paper, there is an matrix whose element has a square root of number operator, e.g. A = \left( \begin{matrix} \alpha & \gamma \sqrt{\hat{a}\hat{a}^\dagger} \\ -\gamma \sqrt{\hat{a}^\dagger\hat{a} & \beta \end{matrix} \right) where \alpha, \beta, \gamma are real...
  15. S

    Integral involving a square root which I can't work out

    Homework Statement Hi, I'm stuck on the following integral. ∫ y / (√(a(y^2)-c)) dy where a and c are constants Homework Equations The Attempt at a Solution I've tried using standard integrals involving square roots in the denominator, but I'm unsure what to do with the y on...
  16. H

    Constructible root from cubic polynomial

    Does x^3 - 3x + 3sqrt(3) = have a constructible root? my solution: suppose a is a constructible root of the equation above. we square both sides to get x^6 - 6x^4 + 9x^2 = 27. since a is constructible, a^2 is constructible as well and we can turn this equation into cubic poly with rational...
  17. Z

    Integral involving sine and root

    Homework Statement \int_0^{\infty} sin(ax) / sqrt(x) dx Homework Equations The Attempt at a Solution I thought of using integration by parts, but that gets me nowhere. I'm not sure how to go about this problem.
  18. L

    U-th root of 1/u as u goes to infinity is 1.

    Is this true? n,m\in\mathbb{N} \lim_{n\to\infty}\sqrt[n]{\lim_{m\to\infty}\frac{1}{m}}=\lim_{n\to\infty}\lim_{m\to\infty}\sqrt[n]{\frac{1}{m}}=\lim_{u\to\infty}\sqrt[u]{\frac{1}{u}}=1 Thanks
  19. Y

    Prove sq root of 2 + sq root of 3 is irrational

    hi,i read the post of sq root of 2 + sq root of 3.i understand tat i should use contradiction to solve it.yet,i stuck halfway when i tried to solve it. sq root 2 + sq root 3 = p/q 2 + 2*sq root 6 +3=p^2/q^2 5+2*sq root 6 = p^2/q^2 wat should i do after this?i hav to prove that the addition...
  20. G

    Finding the square root of a+bi (complex number)

    I was reading Roger Penrose' book "The Road to reality". He mentioned the square root of a+bi in terms of a and b. I am trying to figure his answer out for my self but am struggling. Here goes:(x+yi)^2=a+bi x^2+2xyi-y^2=a+bi x^2-y^2=a 2xy=b I can't rearrange these two equations to get x and...
  21. D

    Find the minimal polynomial with real root

    Find the minimal polynomial with root 21/3 + 21/2. I would just use maple but I do not have it installed on this machine. I found the polynomial and verified that this is indeed a root. I only have Eisenstiens criterion for determining whether it is irreducible, and I can not apply it in...
  22. T

    Square Root Problem: Solving for m in s=k√(1+m)/(1-m) | Help & Tips

    Homework Statement s=k\sqrt{\frac{1+m}{1-m}} , solve for m Homework Equations The Attempt at a Solution Honestly I am stumped, but I do know there is a trick to it. I can't quite remember, but it might have something to do with taking the reciperical or the inverse...maybe the...
  23. S

    How Do You Differentiate (sqrt(x))^x?

    I can't figure out Derivative of (sq. rt of x)^x Can anyone help me?
  24. W

    Integral involving square root -

    Homework Statement integrate sqrt(1-x^-2/3)^1/2. Homework Equations The Attempt at a Solution The only thing I can think of is u substitution with u = 1 - x^-2/3. Obviously this cannot work because du differs by more than just a constant. I guess I need to somehow factor...
  25. M

    Root Locus of Unity Feedback Transfer Function: Find K Range for Stability

    I want a MATLAB code to draw the root locus for a characteristic equation of a transfer function of unity feedback, also what is the range of K that keeps the system stable , here is the characteristic equation: s^5+600s^4+50000s^3+ks^2+24ks+80k=0 please help, thanks in previous
  26. B

    Root vs. ratio in determining radius of convergence of a power series

    Hi everyone :smile: When determining the radius of convergence of a power series, when should I use the ratio (a[sub n+1] / a[sub n]) test versus the root (|a[sub n]|^(1/n)) test? I know that I'm supposed to use the ratio only when there are factorials, but other than that, are these tests...
  27. B

    Why is the Square Root of a Real Number Positive?

    Hi, Apologies for the trivialness of the question, but I'm not so great at this. I was wondering why the square root of a real number is positive. Why is sqrt(9) = 3, and not -3 as well, since (-3)² would give 9. Is it just a condition you set, that the function values must be positive? At...
  28. J

    Celebrate Square Root Day: 3/3/2009!

    Happy Square Root Day all. Today, 3/3/2009, is square root day because 3 \times 3 = 2009. That's as good a reason to have friends over for a beer as any. http://www.myfoxdc.com/dpp/news/dpg_Math_Fans_To_Celebrate_Square_Root_Day2223492"
  29. N

    Unique nonneg. square root for nonneg. real number

    Hello, No exclamation mark after hello I'm afraid, I'm frustrated with the following proof. Okay, here's the theorem first: Every nonnegative real number a has a unique nonnegative square root. Here's the start of the proof, pretty much as they have done it but slightly condensed, all...
  30. M

    Reason for dividing peak value by sq. root 2 to get RMS

    I NEED TO GET A DERIVATION SO THAT I CAN MATHEMATICALLY UNDERSTAND WHY: The peak voltage or current is divided by square root 2 to get the root mean square value.please i need a simple derivation just to understand,i will be very greatful for ur consideration.thankyou.
  31. T

    How can the root integral be simplified to a more manageable form?

    \int \frac{dx}{x(1+2\sqrt{x}+\sqrt[3]{x})}=\int \frac{dx}{x(\sqrt{x}+1+\sqrt{x}+\sqrt[3]{x})}= \int \frac{dx}{x(\sqrt{x}+\frac{(1-x)}{1-\sqrt[3]{x}})} i got read of one root but instead i got another one ??
  32. T

    How Do You Simplify Complex Root Integrals?

    i tried this: \int \frac{1-\sqrt{x+1}}{1+\sqrt[3]{x+1}}=\int \frac{1-\sqrt{x+1}}{1+\sqrt[3]{x+1}}*\frac{1+\sqrt{x+1}}{1+\sqrt{x+1}}*\frac{1-\sqrt[3]{x+1}+(x+1)^{\frac{3}{2}}}{1-\sqrt[3]{x+1}+(x+1)^{\frac{3}{2}}} but when i got read of 2 roots i got another two roots which are more...
  33. F

    Proving a Factor of Complex Cube Root of 1 in x^3 + y^3 + z^3 - 3xyz Equation

    Homework Statement If w is a complex cube root of 1, prove that x + wy + w^2z is a factor of x^3+ y^3 + z^3 - 3xyz, and hence factorise the equation completely. Homework Equations Complex cube root of 1 = -1/2 +/- 3^1/2/2 i The Attempt at a Solution Erm, I feel way over my head...
  34. M

    I think linear approximation? (square root, tangent, e^x)

    Homework Statement the value of f(x) = (sqrrt e^x +3) at x=0.08 obtained from the tangent to the graph at x=0 is...? Homework Equations The Attempt at a Solution i used linear approximation. (sqrrt e^o +3) + (1/2(sqrrt3+e^0)(0.08) i got an answer but i know its wrong. i...
  35. redtree

    Root mean square (RMS) of a sinc function

    Given that the root mean square (RMS) of a sine function is as follows: RMS of (a*sin(\omega*r) = a / \sqrt{}2 Let a = 1/\omega Thus RMS of ((1/\omega)*sin(\omega*r)) = 1 / (\omega*\sqrt{}2) But for sinc(\omega*x), what is formula for the RMS?
  36. D

    Integration with fraction and square root

    i am given this function and need to integrate it \frac{4x+7}{\sqrt{-4x^2+20x-9}} i have been trying to intergrate it by calling something T, preferably the expression under the sqrd root, or part thereof (-4x2+20x=T) but i can't find the way to do this, can't find the best expression that...
  37. moe darklight

    Square Root Of 2 Irrationality Proof

    Hi, I'm having trouble understanding some statements in this proof from my textbook: "Thus, 2 = s^2/t^2 and 2t^2 = s^2. Since s^2 and t^2 are squares, s^2 contains an even number of 2's as prime factors (This is our Q statement), and t^2 contains an even number of 2's. But then t^2 contains an...
  38. G

    Rearranging an equation, It includes a square root.

    I want to find the value of r such that: sqrt[(r^2)+(110^2)] + r = 160 Is there a way of doing it? I have found a solution through trial and error (1dp). But I want a method of finding an exact answer. Thanks
  39. S

    Can Anyone Help Identify This Series and Explain MATLAB's Incorrect Answer?

    I have to find the "second smallest root" of the following equation : 1-x+(x^2)/(2!)^2-(x^3)/(3!)^2+(x^4)/(4!)^2+...=0 Matlab returns quite a satisfactory answer. >> p=[1/518400 -1/14400 1/1576 -1/36 1/4 -1 1] p = 0.0000 -0.0001 0.0006 -0.0278 0.2500 -1.0000 1.0000...
  40. B

    Derivative of the square root of xy

    Homework Statement What is the deriv. of the square root of (xy)? Homework Equations The Attempt at a Solution I used the chain rule: (1/2)(xy)^(-1/2) times (y + x(dy/dx)) i am unsure on how to distribute this correctly
  41. I

    Finding Complex Roots: Showing 1 Has Three Cube Roots

    Homework Statement let the complex number 1 = 1 + 0i. Show this number has three cube roots. Use any means to find them. Homework Equations not sure. cubic root x means there is some number y, x = y*y*y. The Attempt at a Solution Well one root has to be 1 Another is...
  42. S

    Is there a simple way to determine if an element is a primitive root modulo n?

    Is there an easy (by which I mean an algorithm polynomial in size of input) way to know whether in the multiplicative group of integers mod P (P is a prime), whether an element is a generator or not?
  43. C

    Root Mean Square Voltage Multiplied by \sqrt{}2: Explained

    Homework Statement An AC generator produces a voltage of peak value V. The frequency of rotation of the coil of the generator is doubled. The r.m.s. value of the voltage produced is Homework Equations The answer is V multiplied by \sqrt{}2 but I don't understand why. The Attempt at...
  44. I

    Square root of a square plus 1

    Homework Statement prove that if n is a natural number greater than 0, then sqrt(n^2 + 1) is not a natural number. Homework Equations The Attempt at a Solution I can't tell if I am right, which probably means that I am not. Assume sqrt(n^2+1) is a natural number. Then there is...
  45. moe darklight

    Square Root Of 2 (from Hardy Course Of Pure Mathematics )

    Square Root Of 2 (from Hardy "Course Of Pure Mathematics") I was surprised to find it in my local bookstore amidst math "cheat" books in the one-shelf math section (and the fact that it was the last copy left... ??). Is he asking to simply carry out the calculation? Or is he asking to...
  46. Q

    Fundamental equations that are at the root of all physics?

    Hi all :D, Is there such a thing as fundamental equations that are at the root of all physics? Thanks PS If yes- then please provide a link to it if possible. Thanks
  47. A

    Root of Non-Linear Eqn (Numerical Method)

    Hi, I have a non-linear function F: \Re^{3}\rightarrow\Re. I would like to find the roots of this equation numerically, since an explicit formula cannot be derived. As far as I am aware Newton's method can only be utilized when the domain and the range of the function are of the same...
  48. T

    A recursive root convergions question

    i wrote the question and how i tried to solve it this link http://img514.imageshack.us/img514/5053/img9151yd0.gif
  49. R

    Square Root Simplified: Methods for Calculating Square Roots by Hand

    Hi, I was taking a square root of a fraction and I was wondering how to get a fraction result after I've taken the square root of it. And it also made it think; How do I take a root of a number in pen and paper, without the use of calulators? Can anyone help me? Thanks
  50. S

    Igor Pro Root Finding: A Physics Major's Guide

    We've been learning Igor Pro in my computational physics class. I'm a physics major but have no background using code to write programs. So far my instructor has basically walked us through how to set up basic programs to graph functions using a graph panel. Now he wants us to make a Root...
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