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. A

    How can the integral of the square root of t squared plus 9 be evaluated?

    Homework Statement \int \sqrt{t^2+9} Homework Equations The Attempt at a Solution Apparently you can't solve this equation as you would \int \sqrt{t+9}, which would come out to \frac{2(t+9)^3/2 }{3}. Instead, my calculator is getting this extremely complicated answer involving ln functions...
  2. V

    The root numbers in toothpaste (help)

    Pardon me for not using latex. Homework Statement A toothpaste box has square ends. The length is 12cm greater than the width. The volume of the box is 135cm^3. What are the dimensions of the box? Homework Equations Quadratic theory, Random pluggin for x, common factoring, Family of...
  3. G

    Square Root in Special Relativity

    Can anyone explain what the square root does? I know 3 squared equals the square root of 9. I want to learn what is actually happening behind the math, if that makes sense. Consider the following: I’m calculating the wavelength of light, and traveling towards the source. Speed of light =...
  4. M

    Finding F'(x) for Square Root of x

    Homework Statement F(x)= square root of x what would F'(x)=? (F prime of x) Homework Equations F(x)= 3x^2 F'(x)=6x F(x)= x^3 F'(x)=3x^2 The Attempt at a Solution no clue. If the variable is a square root, it wouldn't have an exponent, right? confused.
  5. T

    Solving a Root Equation for the Variable r

    Hi, I have the equation A = πr² + r²root(k²-1) i need to rearrange it to find r i go it to r³ = (2A/π+root(k²-1) to get just r (with no powers) what will the final equation look like and why. Thanks :biggrin:
  6. A

    MATLAB Finding Root of 8x^3-36x^2+54x-12=0 Using Bisection Method

    Hi, Im new to Matlab, and my lecturer asked me to do his question which is: Find one root of equation 8x^3-36x^2+54x-12=0 using the bisection method. Your answer must includethe number of iterations. Ive already read the Introduction to MATLAB 7, and Numerical Methods for Engineers. And...
  7. A

    Absolute value and square root

    what is /squared root sign4x+1 / what does this equal because I'm confused when it has the square root sign on it all and it's absolute value
  8. G

    What is the solution to (2-11i)^(1/3)?

    Homework Statement I need to find the solution to (2-11i)^{\frac{1}{3}} Homework Equations If (2-11i)^{\frac{1}{3}} were to equal (a + bi) for some real numbers a and b then 2 - 11i = a^3 +3a^2bi-3ab^2-b^3i The Attempt at a Solution From above a^3-3ab^2 = 2 and 3a^2b - b^3 =...
  9. L

    Square Root of Complex Numbers

    Hi! I've got a question. There is a nice formula for finding square roots of arbitrary complex numbers z=a+bi: \frac{1}{\sqrt{2}}(\epsilon\sqrt{|z|+a}+i\sqrt{|z|-a}) where epsilon:=sing(b) if b≠0 or epsilon:=1 if b=0. I've just looked it up and it's nice to use it to find complex roots of...
  10. M

    What is the Use of deMoivre's Formula in Finding Roots of Complex Numbers?

    wat is under root - i ? please anser this
  11. mattmns

    Root and Ratio tests Inconclusive

    Here is the question in the book: -------------- Give an example of a divergent infinite series of positive numbers a_{n} such that \lim_{n\rightarrow \infty}a_{n+1}/a_{n} = \lim_{n\rightarrow \infty}a_{n}^{1/n} = 1 and an example of a convergent infinite series of positive numbers with the same...
  12. S

    Discrete Weighted Transform - A Primitive Nth Root of Unity

    Hello, I got pointed to this forum by OfficeShreder. I have a question I've been puzzling myself over for a while. I am currently trying to implement the "Discrete Weighted Transform". I have reached a step where I need to determine "a primitive Nth root of unity in the appropriate domain"...
  13. murshid_islam

    What is the square root of i^2

    what does \sqrt{i^2} equal to? is \sqrt{i^2} = i or \sqrt{i^2} = \pm i?
  14. U

    Is the square root of a prime number always going to be irrational?

    is the square root of a prime number always going to be irrational? just a random question.
  15. T

    Finding the Greatest Integer Square Root of an Integer

    Consider the square root operation. Suppose an integer numbers i > 0 as input variable. Design an algorithm which calculates the greatest natural number less than or equal to the square root of the input variable i. can smby pls explain to me what does this ques mean??if possible explain...
  16. K

    Quadratic Equations with positive root

    How do you solve quadratic equations which have atleast one positive root?? The question was this: Find the value of 'm' for which the roots are such that at least one is positive. x2 -(m-3)x + m = 0 mR. Can someone help me get started? Here is my work: I checked the discriminant. for...
  17. P

    How can I simplify sqrt( 4t^2 + 4 + ( 1/t ) ) to (2t^2 + 1)/t?

    Couldn’t decide if I should put this in the calculus or general math forums but... I’m studying for a final that’s coming up this Wednesday and I’ve been looking at some past quizzes with the steps to finding the solutions that my instructor has posted online. Given the problem: 1. Compute...
  18. N

    What Does the Area Under the Molecular Speed Distribution Curve Represent?

    hi guys i gota question in chemistrygas laws , i thought about it and am still confused ~~~~~~~~~~~ what does the area under a number of molecules against speed of gas represent? it is to do with root mean square speed ... i thought that it might be the average kinetic energey but it seems...
  19. D

    Show equation has exactly one root

    The question is show that the equation f(x)=3x-2+cos(Piex/2)=0 has exactly one real root. Using the intermediate value theorem f is continuous and f(o)=-1 and f(1)=1., the equation has one root. Supposing it has two roots a and b , and a<b. Then f(a)=0=f(b). Using Rolle's theorem there is a...
  20. P

    Find the square root of a quantity in what unit

    Hey all, this is my first post here, I have just discovered the site, and it looks great :smile: I need some help on units, regarding square roots. When you find the reciprocal of a quantity, like say, mass, the new unit is kg-1. I'm not sure about when you find the square root of a...
  21. J

    How Do You Integrate the Square Root of Tan x?

    My class, teacher included, cannot seem to figure out the integral of the square root of tan x. Maybe someone here can help? thanks, jeremy
  22. N

    MATLAB Matlab and Root Mean Square help

    Matlab and Root Mean Square help please... So I have this given data: year = [1928:4:1936 1948:4:1956 1964:4:2000]; time = [12.2 11.9 11.5 11.9 11.5 11.5 11.4 11.08 11.07 11.08 11.06 10.97 10.54 10.82 10.94 10.75]; and after plotting it (time vs. year), I am told to find the best...
  23. A

    Sketch the graph of the function f(x)=square root X

    a) sketch the graph of the function f(x)=square root X b) on the same set of axes, graph y=f^-1(x), y=-f^-1(-x) so I did a chart, but i don't know if its right...I don't think its right :confused: f(x)=squareroot x X Y 0 0 1 1 4 2 9 3 y=f^-1(x) X Y 0 0 1 -1...
  24. U

    What is the root mean square average?

    Uing a probability distribution for values obtained in throwing 3 dice together, find the uncertainty associated with throwing th 3 dice togehter, that is, the root mean square average of the deviation of a given thrown from the average throw. What exactly is "the average throw" ? I know what...
  25. F

    Root Locus: Get Help with State-Variable Feedback Design

    I had to use state-variable feedback to design a position control system for a motor. I have to design the controller using root locus methods. The gain that is varied is located in the feedback loop as shown in the picture. I am completely lost as to how to generate a root locus with the...
  26. F

    Help with Root Locus: Get into General Form for Drawing

    I had to use state-variable feedback to design a control system for a motor. I first designed a deadbeat controller, which was pretty easy. But now I have to design another controller using root locus methods. The gain that is varied is located in the feedback loop as shown in the picture...
  27. C

    Sequence based on sequential square root function

    Express each term of the sequence \{\sqrt{2}, \sqrt{2\sqrt{2}}, \sqrt{2\sqrt{2\sqrt{2}}}, ...\} as a power of 2. I found \{2^{\frac{1}{2}}, 2^{\frac{3}{4}}, 2^{\frac{7}{8}}, ...\} but I can't get the formula for it so I can find it's limit.
  28. S

    How do I integrate inverse root functions in calc 2?

    I am taking calc 2 and I think we just finished up all the different ways of integrating, yet I can't figure this seemingly very simple one out. Any help is greatly appriciated.o:) \int\sqrt\frac{1}{x}dx
  29. F

    What is Causing the Exponential Curve in My Velocity Squared vs. Radius Graph?

    Hey-- I'm writing up a physics lab report on centripetal force; at the moment I've hit a problem with the velocity squared vs. radius graph. The graph *should* show a root curve (v^2 = Fr/m) but all of the regression utilities I've used churn out an exponential curve. Here are the four points...
  30. N

    Is the Book Wrong? - Square Root of 4

    hey guys on my textbook, it says that square root of 4 equals to 2 but not negative 2. The book is wrong right?
  31. T

    Sqr root of (x-4)^2 + y^2, what do we use this for?

    does anybody knows what does the eqn such as sqr root of (x-4)^2 + y^2 use to find for?? pls help...
  32. D

    Another simple square root problem

    why is the square root of 25 just 5 but when the question x^2 = 25, the answer becomes +/- 5? whats the logic here? i don't quite get it. thanks.
  33. D

    Can You Multiply Square Roots of Negative Numbers?

    suppose you have square root of -16 times square root of -25 (in separate square root symbols). would the answer be: a) no solution - can't have negative square roots b) 4i times 5i which equals 20i^2 which is -20 c) -16 times -25 which is +400, then the square root of that is 20...
  34. R

    What are some other roots for the tree of evil?

    I hold that the "root of all evil" (for humans) is when a human uses another human as a means to an end, even if those being used agree. Comments -- other roots for the tree of evil ?
  35. J

    Connection between root and branch

    It is rather well known that the color of flowers on Hydrangea depends upon the pH of the soil in which it is planted. Low pH in the soil means blue flowers and high pH means pink. Here is a quote from the Texas A&M site on Hydrangea: Sometimes a single plant may have shades of both pink and...
  36. P

    Proof of Rational Root Theorem

    I want to find a nice and elegant proof of the Rational Root theorem, but I get stuck. I read some stuff on the Internet, but I have not found a complete proof of the theorem. Here's my try: Say we have a polynomial: F(x) = \sum ^{n}_{r = 0} a_{n}x^{n} = a_{n}x^{n} + a_{n - 1}x^{n-1} +...
  37. A

    Solving a cubic (or rather simplifying a real root in complex form)

    The determinate of the following 3x3 matrix 1-y, 2 , 3 2 , 4-y, 5 3 , 5 , 7-y gives a cubic that simplifies to, y^3 - 12*y^2 + y + 1 = 0. Now, apparently the teacher picked random numbers for the original matrix, making the problem delve into other realms of mathematics...
  38. M

    How do you solve x^2 + 2 = 0 and x^4 + 4 = 0?

    Find all real/imaginary roots to x^9=16x
  39. U

    What is the square root of complex numbers?

    Please help with these simple questions just not understanding it properly. Find square root, of -6i let sqroot of -6i= x+ yi then -6i=x^2 - y^2 +2xyi x^2 - y^2 = 0 and 2xy=-6 then xy=-3 x=-3/y and then solve simu.. i got y= 3 and x=-1 y=-3 x=1 so the anser is +_(-1+3i) BUt that...
  40. Artermis

    What Happens to Beet Root Pigments When Cells are Disrupted with Chloroform?

    Quote: Originally Posted by Artermis Hello Moonbear, I don't know if you know me but I'm a relatively new member but I know that you are very knowledgeable and helpful, hopefully you'll be willing to help me with this. Hi, I've seen you in the biology forum recently. Glad to have you...
  41. E

    Programming TI-83 for Reimann Sums: Y1=\sqrt{1+sin^3}

    I'm trying to program my 83 for Reimann sums and I believe I've got it now but to plug in for Y1= \sqrt{1+sin^3} how do I make the \sin^3 part because the parenthesis keep me from getting the ^3. I've tried the MATH button but it won't work that way.
  42. L

    Irrationality of the square root of a prime

    I saw a proof saying the root of a prime is always irrational, and it went something like this: sqrt(r) = p/q where p/q is reduced r = p^2/q^2 r*q^2 = p^2 therefore, r divides p so define p = c*r r*q^2 = (c*r)^2 = c^2*r^2 q^2 = c^2*r therefore, r divides q also since r divides p...
  43. N

    Prove the Square Root of 2 is irrational

    This is Algebra 2 question... I have to prove that the square root of 2 is irrational... First we must assume that sqrt (2) = a/b I never took geometry and i don't know proofs... Please help me. Thank you.
  44. T

    Unraveling the Mystery of Solving Square Roots

    I'm just wondering about something, look at this: \[ \begin{array}{l} \sqrt {3 + x} + \sqrt {2 - x} = 3 \\ \left( {\sqrt {3 + x} } \right)^2 + \left( {\sqrt {2 - x} } \right)^2 = 3^2 \\ 3 + x + 2 - x = 9 \\ 5 = 9 \\ \end{array} \] Obviously something isn't right...
  45. E

    Draw a Line of Length √3: Tips from an Old Man

    An old man gives you a set square (http://www.buchhandlung-umbach.de/pbs/geodreick.gif ) and then asks you to draw a line of exactly the length \sqrt{3} . How would you do it?
  46. M

    Find a root for this expression:

    cos(x)+cos(ix)+cos(x*i^3/2)+cos(x*i^1/2)=0 for x I have spent a lot of time finding an analytic root to this equation without success. An analytic root may not exist. I don't know. It is roughly equal to (8facorial)^(1/8)
  47. K

    F(t) = square root of 3t+2 / 4t-3

    Need to find the derivative of: f(t) = square root of 3t+2 / 4t-3 please help.
  48. I

    Is x Irrational When x^x Equals 2?

    How do I show that 2 has no rational roots?
  49. Z

    How to find properties of root hard disk?

    Start Windows Explorer, right-click the computer's root hard disk, and then click Properties how do I find the computer's root hard disk in order to righ click on it?
  50. C

    Can a Triangle Have Sides of 1m and Hypotenuse of √2m?

    Square root of 2... Is it actually possible to produce a right angled triangle with sides exactly equal to 1m and 1m? Because this would produce a hypotenuse with length "square root of 2" m, which has no exact length. Thanks in advance. :smile:
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