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. C

    Solving the Mystery of i & j: The Square Root of -1

    Square root of -1... We say that the square root of -1 is equal to i ( or j ), and that this is therefore not a real number - but what is this fact actually useful for? Why over complecate things with something not on the number line - why is it so useful to treat the square root of -1 as a...
  2. C

    Derivative of f(x)=(square root x^2-2x)^3-9(square rootx^2-2x)

    How do I find the derivative of f(x)=(square root x^2-2x)^3-9(square rootx^2-2x)
  3. T

    I'm sorry, I'm not sure what your question is. Could you clarify?

    Hi, I'm trying to find this integral: \int \frac{x}{(x+1)\sqrt{1-x^2}}\ dx Because 1-x^2 has two different real solutions, I can write \sqrt{ax^2 + bx + c} = \sqrt{-a}(x_2 - x)\sqrt{\frac{x-x_1}{x_2 - x}} so \sqrt{1-x^2} = (-1 - x)\sqrt{\frac{x - 1}{-1 - x}} = (-1 -...
  4. Orion1

    Proving One Real Root for 2x - 1 - sin x = 0

    Show that the equation: 2x - 1 - \sin x = 0 has exactly one real root. \frac{d}{dx} (2x - 1 - \sin x) = 2 - \cos x = 0 2 = \cos x x = \cos^{-1} 2 Is there a better way to approach the root? any suggestions?
  5. A

    Square Packing Solutions for 24 Integer Squares

    \begin{array}{c} {{A_n}={\sqrt{\sum _{z=1}^{n}{z^2}}} } \\ {{A_1}=1 } \\ {{A_{24}}=70}\end{array}\ Is there a proof that only for n =1 or n=24 that An is an integer quantity?
  6. A

    Understanding Imaginary Roots in Complex Numbers

    hi i was trying to determine the sqrt of -1,and here is wat i have done. sqrt of -1=-1^2/4,this further gives [[-1]^2]^1/4, which further gives 1^1/4 therefore the sqrt of -1 is 1^1/4 which is 1 have u any objections,let me know
  7. D

    What is the Simplest Way to Find the Square Root of i?

    Does i, the imaginary number, have a square root? This was bothering me for a while, then I thought I happened upon a simple solution, but have since forgetten. \sqrt{i}=?
  8. L

    Need proof that a cubic equation has at least one real root

    Hi, A cubic equation has at least one real root. Can someone help me to prove this? Thx! LMA
  9. B

    Understanding the Limit of Recursive Sequence R_n for x = k^2 - k + 1

    Short root sequence question For the recursive sequence R_n = x + \sqrt {x - \sqrt {R_{n - 2} } } R_0 = x = k^2 - k + 1 \forall k \in \mathbb{N},\;k > 1 why does \mathop {\lim }\limits_{n \to \infty } R_n = k^2 ??
  10. M

    Find the square root of negative numbers

    I don't get the use of imaginary numbers. To find the square root of negative numbers but it does not exist and it is not a real number. Can u please explain it to me.
  11. T

    Root of a complex number in cartesian

    Is there any law for finding the root of a complex number in catesian coordinates? without changing to polar, I've created 1, i just want to know is it worthy or not, so ... everybody who reads the message, please post the ROOT OF A COMPLEX NUMBER IN CARTESIAN COORDINATES LAW and let me...
  12. E

    Proving the Relationship Between Integrals and Root Pi Using Multiple Integrals

    A problem in my textbook guides you through this proof using a multiple integral. I follow the whole thing except for one step. It requires that you show that (sorry don't know latex, I(a,b) will denote integral from a to b, e the exponential) [I(-x,x)e^(-u^2)du]^2=I(R)e^(-u^2-v^2)dudv...
  13. T

    Square Root of x^9 ≠ x^4.5: Exploring the Difference

    Why is it that the square root of x^9 for some x isn't always the same as x^(4,5) ? I tried to do this with x=12 on my TI-89 and it comes very close, the difference comes after like the 8th decimal or something, but shouldn't it be excactly the same?
  14. N

    Simplifying Loga Root Expression

    Simplify 1/2[Loga N - Loga (N - 1)] I get something like 1/2[Loga N / (N-1)] Loga root[ N / ( N-1 ) Loga root [ (N * ( N + 1)) / N^2 - 1 ]
  15. L

    Proving Algebraic Nature of Root 3 + Root 2

    I need to show that this is an algebraic number. In other words, I need to show: an*x^n + an1*x^(n-1) + ... + a1 * x^1 + a0 * x^0 = where the a terms are not ALL 0 but some of them can be. Like for root 2 by itself, I have 1 * (root 2) ^ 2 + 0 * (root 2)^1 + -2 * (root 2) ^ 0...
  16. L

    Proving an Algebraic Number: Root 3 + Root 2

    I need to show that this is an algebraic number. In other words, I need to show: an*x^n + an1*x^(n-1) + ... + a1 * x^1 + a0 * x^0 = where the a terms are not ALL 0 but some of them can be. Like for root 2 by itself, I have 1 * (root 2) ^ 2 + 0 * (root 2)^1 + -2 * (root 2) ^ 0...
  17. L

    Proving the Algebraic Nature of Root 3 + Root 2 Using Polynomial Expressions"

    I need to show that this is an algebraic number. In other words, I need to show: an*x^n + an1*x^(n-1) + ... + a1 * x^1 + a0 * x^0 = where the a terms are not ALL 0 but some of them can be. Like for root 2 by itself, I have 1 * (root 2) ^ 2 + 0 * (root 2)^1 + -2 * (root 2) ^ 0
  18. L

    The irrationality of the square root of 2

    I saw this proof in class today to prove the square root of 2 is irrational: 1. Assume that √2 is a rational number. Meaning that there exists an integer a and b so that a / b = √2. 2. Then √2 can be written as an irreducible fraction (the fraction is shortened as much as possible) a...
  19. A

    A little inverse help cube root

    find the inverse of f(x)=3sqrt(x+2) -7 x>=-2 I got this far (x+7)=3sqrt(y+2) I don't know how to get rid of the cube root someone help please :cry:
  20. E

    Plotting Root Mean Square Calculations with Radians

    I tried some formulas on my graph calculator after reading about root mean square calculations of power and physics. Plot these using radians: Y1 = (sin(X)^2)^(1/2) Y2 = (tan(X)^2)^(1/2) Y3 = (tan(X)^3)^(1/3) Axis: 0<x<2(pi) 0<y<2(pi) or zoom to fit! kinda cool huh! Has anyone...
  21. B

    Solving the Primitive Root Problem for g & -g Modulo p

    let g be a primitive root of the odd prime p show that -g is a primitive root or not according as p==1 ( mod 4) or p==3(mod4) how would i start in solving this problem thanks :cool:
  22. C

    Quadratic Formula: Negative in root?

    What do you do when Root(b^2-4ac) is negative? because you can't have a negative under a root right?
  23. V

    Transforming Equations to Solve for Unknown Variables for Scientists

    \sqrt{x} + \sqrt{x+2} + \sqrt{x}\sqrt{x+2}=16,5-x
  24. A

    What value of k gives no roots,one root, 2 roots?

    roots! HELP For what values of k does the equation x^2+k=kx-8 have two distinct roots, one real root, no real roots? convert into standard form first well x^2+k-kx+8 I don't know if i can simplify this further? and if i can't then what does a=? b=? and c=? I don't understand how to do...
  25. A

    Find Square Root: 5+12i Calculation

    does anyone know how to find the square root of 5+12i ?
  26. D

    Solving Fifth Roots of z = 1 + √2

    Here's a silly roots question that has my congested mind temporarily stumped: Let z = 1 + \sqrt{2}. Find the five distinct fifth roots of z. Thanks in advance for helping me relieve the pressure.
  27. T

    How to Prove This Limit with Cube and Fourth Roots?

    Hi guys, I have another limit I can't move with. Well, I guess it goes to zero, but can't show a bulletproof evidence: \lim_{n \rightarrow \infty} \frac{ \sqrt[4]{n + 2} - \sqrt[4]{n + 1}}{ \sqrt[3]{n + 3} - \sqrt[3]{n}} Even after I got rid of denominator, I can't find some known...
  28. C

    Proof of limit involving square root

    Hello all I am having trouble proving the limit of the following: lim sqrt(( n+1) - sqrt(n)) * sqrt(n+ 1/2 ) = 1/2 n --> 00 I tried using the fact the the limit of the first factor as n approaches infinity is 0. Then I tried expressing the first factor as 1 /...
  29. A

    Is the Square Root of 0 Undefined?

    Is the square root of 0 undefined? I was recently told that the square root of 0 is undefined because the limit of a square root didn't exist at 0. The reason is that from the negative direction you have i and from the positive direction you don't. At first, i agreed with this. It made enough...
  30. N

    Life: Comparing Chloroplasts in Onions and Other Plant Cells

    Which organelles do mesophyll cells have more than root cells of a plant? Do Onions have chloroplasts?
  31. F

    Integrating nested root in denominator

    Hi Y'all, I was trying to integrate a function in two dimesions. after integrating it in one dimesion and substituting the limits I got two terms. I am unable to integrate the second term. That is because it had a sqare root in the denominator which contained another one within it. I took...
  32. O

    Simple square root factoring question

    Hi, is \sqrt{a^2-a^2\sin^2{x}} = a\cos{x}? If not, what should it be? :confused: Appreciate the help! :smile:
  33. F

    What are the strategies of root competition in the forest?

    I learned that trees and plants compete for survival just like other species. They compete for sunlight and nutrients in the soil. If you're a tree who wants to catch some rays, the goal is to grow as big and tall as possible, and make the enemy trees eat shade. But how do they compete for...
  34. H

    Root Theorem for Polynomials of Degree > 2

    What is the theorem that states if \Omega is a polynom with degree > 1 with real coefficients. If there exists a complex number z = a + bi such that \Omega(a+bi)=0 then \overline{z} = a - bi is also a root of \Omega ? For \Omega(x) = x^2 + px + q with p and q real then if a+bi is a...
  35. S

    Simple question about writing a log-how does the root go turn to divison?

    Simple question about writing a log--how does the root go turn to divison? I understand the product, quotient and power laws of logarithms. But this piece in the book has me stumped. It says how they used logarithms to rewrite calculations and make them easier to figure out. Fair enough...
  36. S

    Polynomial find the range of root

    The question is : Show that one of the root of the equation y^3 - 3y + 4 = 0 lies between -3 and -2. REMEMBER : If you want to use some statement, Law, identity or logic, please PROVE it first before you proceed to answer the question.. Difficulty for me is, normally we are asked to solve...
  37. I

    Solve a radical equation where the root is a negative integer?

    Is it possible to solve a radical equation where the root is a negative integer?
  38. I

    Square Root of Pi: Is it Possible?

    The square root of pi is 1.777245... I know. But my math teacher says its impossible to determine a square root of an irrational number. Can anyone shed any light on this? is it or is it not possible to determine the square root (or any root) of an irrational number?
  39. M

    Finding Principal Root of \sqrt[3]{8i}: Stuck at Arctan?

    I have to find the principal root of \sqrt[3]{8 i} But I get stuck at this part change this to polar coordinates... r= \sqrt {x^2 + y^2} which makes r=8 but when I try to find \theta \theta = \arctan \frac{y}{x} from the original x = 0 so how do I find \theta?
  40. J

    Root Mean Squared: Definition & Formula

    What is the concept of root mean squared all i got were i bunch of formulas saying this equals that
  41. M

    Is the Sum of Square Roots of 2 and 3 Irrational? A Proof by Contradiction

    Yeh just having a problem seeing a way to prove that 6^(1/2) is irrational. Using this answer and proof by contradiction I need to prove that 2^(1/2) + 3^(1/2)is also irrational, however I sould be able to attempt this if I can get the above right. Any help much appreciated.
  42. C

    How can we find the root for high degree polynomial functions?

    How do you find the root for high degree polynomial functions? I am really lost on this, any help would be appreciated.
  43. Rockazella

    Noise Calculation in Video Signals: Understanding Sqroot(2)

    Not sure if this is more a question for the physics forum or here, but ill start here. I've been doing some reading on signal to noise calculations for video applications. In the reading it says that when you drop a certain signal by 2, the noise portion of it will only drop by sqroot(2)...
  44. Monique

    Deleting Files from Unix Root & Subdirectories Without Going There

    Hi guys, I have been trying to get familiar with the Unix environment.. there is just one (actually two) things that I cannot figure out. It must be a trivial question for you guys. How do I delete a file from a root directory without actually going there? How do I delete all the files...
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