Root Definition and 944 Threads

You can chart the square roots relative to each other starting with a quarter-circle, a square, and a diagonal line. Where the circle intersects with the diagonal, the next square root is found. http://www.perspectiveinfinity.com/images/rgsteps_w.png More here...

Hi all, How to convert the root of an equation from symbolic form into an ordinary from? I have tried to use the N command, but still displaying in the symbolic form. Thanks

How is squareroot(x)*(1/x)= 1/square root x can somebody please explain this? I think I am having a brain lockup...

Hey all, I've run into a snag with research and it is partly related to taking the square root of a matrix. I've seen related stuff concerning matrices that can be diagonalized, however the 2x2 matrix in question is not diagonalizable. Can the square root of such a matrix be determined? If...

1. For n ≥2, n^(1/n) is irrational. Hint provided: Use the fact that 2^n > n2. This is probably familiar to many. By contradiction, n = a^n/b^n --> a^n = n(b^n) --> n|a^n --> n|a Am I trying to force the same contradiction as with 2^1/2 is rational, that is, that a/b are not in lowest terms? Or...

Homework Statement Let f(x)=x^{1/3} show that it is uniform continuous on the Real metric space. Homework Equations By def. of uniform continuity \forall\epsilon>0 \exists\delta>0 s.t for \forall x,y\in\Re where |x-y|<\delta implies |f(x)-f(y)|< \epsilon The Attempt at a Solution...

Homework Statement Our teacher was talking about something regarding two tangent lines on a circle who distance between the tangent lines is square root of 3 times the radius of the circle... She wanted us to find the proof of this but I am stumped on where to even look... Does anyone know...

As you can't take the square root of a negative number without introducing complex numbers, which would be the correct answer to this function: Equation: x = -2 f(x) = √x / (x(x-1)) Answer a) 1.41i / 6 or Answer b) 0

Homework Statement find the inverse of y=2x^2-8x x>=2 I am in calculus b but forgot some of the algebra so I am not sure how to treat the root Homework Equations The Attempt at a Solution I am skipping steps y=2(x-2)^2-8 (y+8)/2=(x-2)^2 I know that x >=2 so f(2) =-8 and...

Is there a way to simplify this? Is this a known function? tan(arccos(((x/y)-1/y )/ ((x/y)+ 1/y)))*((x/2)-1/2)=sqrt(x)

How to prove that root n is irrational, if n is not a perfect square. Also, if n is a perfect square then how does it affect the proof.

Prove that cube root of 6 irrational. Solution: I am trying to prove by contradiction. Assume cube root 6 is rational. Then let cube root 6 = a/b ( a & b are co-prime and b not = 0) Cubing both sides : 6=a^3/b^3 a^3 = 6b^3 a^3 =...

I'm trying to understand root systems better. They seem to be tied to what I've been working on. Any suggestions on books? here is an e8 root system http://upload.wikimedia.org/wikipedia/commons/thumb/f/fe/E8_graph.svg/500px-E8_graph.svg.png here is some of my root system. the prime...

Banging my head against a wall trying to prove to a coworker why the square root of three shows up in a three-phase voltage drop calculation...any ideas?

Homework Statement show that cos(2pi/n) + isin(2pi/n) is a primitive root of unity Homework Equations The Attempt at a Solution if i know z = cos(2pi/n) + isin(2pi/n) is an nth root and I'm trying to prove that z is a primitive nth root. is it correct to assume that z^k is not...

Is anyone familiar with this method of determining square roots? http://www.cs.cas.cz/portal/AlgoMath/Geometry/PlaneGeometry/GeometricConstructions/SquareSquareRootConstruction.htm I have an equation that I'm working on that expands on this a bit and I'd love some feedback.

Hey there, Square roots never have been my strongest point in maths, but I'm not seeing the trick in this example: I'm trying to find an alternate form of: sqrt(3+sqrt(8)) I get as far as: sqrt(3+2 sqrt(2)) But i know i want to/should end up with: 1+sqrt(2) I just don't know how...

well it is easy to construct sqrt(2) with a triangle with two sides of length 1. but what about sqrt(2 + sqrt(2)) or the iteration sqrt(2 + sqrt(2 + sqrt(2))). the question is how to construct a line with length sqrt(sqrt(2)) i guess(beginning with lines of length 1), but i am not sure.

I arrived at this problem while trying to find the length of a 3D http://en.wikipedia.org/wiki/Cubic_interpolation" . Basically, I'm having to figure out how to integrate ((At4+Bt3+Ct2+Dt+E)1/2)dt A,B,C,D, and E are constants which have to be plugged in after integration, I'm sorry to say...

Homework Statement Helium is used to fill a balloon of diameter 44 cm at 22 degrees C and 0.9 atm. The mass of a helium atom is 4.0026 u, the conversion factor from u to kg is 1.66 x 10^-27 kg/u, the conversion factor from atm to Pa is 1.013 X 10^5 Pa/atm, the universal gas constant is...

Let p be a prime number. Find all roots of x^(p-1) in Z_p I have this definition. Let f(x) be in F[x]. An element c in F is said to be a root of multiplicity m>=1 of f(x) if (x-c)^m|f(x), but (x-c)^(m+1) does not divide f(x). I'm not sure if I use this idea somehow or not.

I am trying to find the domain of this function f(x)=sqrt(x^2 - 2x +5). i am supposing that y=x^2 - 2x +5 and y must be greater of equal to 0. in otherwords where the graph is touching or above x axis. to find where the graph is touching x-axis i am trying to find the x intercept and i get...

When we solve to equations say y2 = 4x and x2 + y2 = 9/4 for x, we get two values - x=0.5 and x=-4.5 The equations represent a parabola and a circle resp. with x=either 0.5 or -4.5 as the abcissae of intersection. I don't understand why do we reject one value which is -4.5 in this case...

Homework Statement I don't know how to find the square root of a complex number in rectangular form? As in, say, \sqrt{}9-6i..my calculator can't do such an operation (yet my graphics calculator can, which can't be used in exams), so how do i go about to do this 'by hand'? I just found...

We can easily comment the result of a root operation just by the information if the degree of the root is odd or even. But what if the degree of the root (or power) is irrational? For example; -64 ^ \frac{1}{2} \, = \, j8 \,\,\,\,\, (imaginary) -64 ^ \frac{1}{3} \, = \, -4 \,\,\,\,\...

I need an algorithm to calculate nth root or power of any given real number. "n" can be either integer or fractional, and is real. I found http://en.wikipedia.org/wiki/N-th_root_algorithm" , but it requires to calculate power in it, therefore I can't use it. Newton's method: x_{k+1} =...

I solved on my own the work below is incorrect.Homework Statement A sealed 500ml flask contains oxygen gas at a temperature of 27 degrees Celsius. a) Calculate the root mean square speed of an oxygen molecule in the flask? b) Calculate the average kinetic of an oxygen molecule in the flask...

At http://www.wolframalpha.com/ , if you type: 1) (-1)^(1/3) It gives a complex approximation. Isn't it exactly -1? David

Homework Statement Show that the equation x3-15x+C=0 has at most one real root in [-2,2] Homework Equations Rolle's Theorem, and Intermediate Value Theorem. The Attempt at a Solution I showed that there is a root in [-2,2] by use of Intermediate Value Theorem. f(-2)<0 f(2)>0...

graph/analyze a function of a rational /w complex root?!? Homework Statement The function is y=x^2/(x^2+3) Homework Equations First and Second Derivatives Chart to find intervals of increase/decrease and concavity. The Attempt at a Solution 1) Domain {XeR} 2) Intercepts If...

a is a root of order k of the polynomial p provided that k is a natural number such that p(x)=[(x-a)^k]r(x), r is a polynomial and r(a) not equal to 0. Prove a is a root of order k of the polynomial p iff p(a)=P'(a)=...=[p^(k-1)](a)=0 and [p^(k)](a) not equal to 0. Note: [p^(k-1)](a) :=...

Hi, ive created several graphs in different emacs files. I now want to superimpose them using code in a different emacs file. This is what i have done: //get the input files TFile * inputfile = new TFile("p60.root","READ"); TFile * inputfile2 = new TFile("p20.root","READ")...

Homework Statement Calculate the area under the curve for the following: f(x) = √x*√(−32 − x) and g(x) = √(−x2 − 32x) Homework Equations The Attempt at a Solution I've been trying to do partial integration since the functions f(x)=g(x)area are mirrored, so they are equal...

Homework Statement * Show that the equation 2x-1-sinx=0 has Exactly one real root. Homework Equations *N/A The Attempt at a Solution *Ok so normally to find the real roots for x I would solve for x when I set the function equals to 0, but with this function there is an x...

http://www.macasex.com/ I saw a bit about this on TV [an investigative report, not a commercial] the other night. Apparently it is common for women in Peru to use Maca root to increase libido. When asked if it works, one women commented, "It will make Chinese fireworks in your pants!". It...

Homework Statement Im having difficulty drawing a specific graph. I am not entirely sure how to explain my question/ the graph i need to draw so i think the best way is to provide a bit of my code and explain using it the graph using it... the code below gives a read out of the energy...

ive been plotting 2D histograms (x vs y). when plotting using Draw->("surf"). it gives a 3D plot, showing the varying number of "hits" in each bin. I want to draw a TGraph which represents this so when drawing x vs y using Tgraph it gives a continuous line instead of a bunch of dots. I've got...

Hi everyone, I would please like some suggestions regarding where my error is, designing a lead compensator with the root locus method for a unity feedback control system where G = [12.5] / [2.5 1 2500]. I want to set the overshoot zeta = 0.5 for an overshoot of 16%, and settling time Ts =...

Homework Statement Really new to complex numbers so please forgive my ignorance. Prove that if the complex number z is an nth root of the real number x then the complex conjugate z (z with horizontal line on top) is also an nth root of x.Homework Equations i2=-1The Attempt at a Solution nsqr(z)...

Hi there, I have over the last couple of month worked my way through Algebra Demystified and College Algebra Demystified (well almost), and I just completed the chapter on polynomial functions and I’m stuck at one of the questions in the chapter review where I’m given a complex root and the...

Homework Statement integrate (xdx)/sqrt(1-x^2) on the integreal [2,5] Homework Equations integral u^n(du) = u^n+1/(n+1) The Attempt at a Solution I'm no good at using latex so I scanned in my work. I get .716 but when I check with my calculator it comes out as 2.863

z_k=\sqrt[n]{u}=\sqrt[n]{r}e^{i\left(\frac{\phi+2k\pi}{n}\right)}, k=0,1,2,...,n-1 and z_k=\sqrt[n]{u}=\sqrt[n]{re}^\frac{\phi+2k\pi}{n}, k=0,1,2,...,n-1 Which one is incorrect (note that in the first, e is out of the root)?

Homework Statement Antiderivative of sqrt[e^x+ln(x^2)+1] Homework Equations The Attempt at a Solution (2[(e^x+ln(x^2)+1)^(3/2)]x^2)/[3(e^x+2x)]

I tried to use tex code but it seems to be caching the image on preview, so anyway dy/dx ( x / root x) = 1 / ( 1/2 x^(-1/2) ) however the answer given to me is just ( 1/2 x^(-1/2). What's gone wrong? Spent an hour on this and now unsure if my algebra is wrong. And the tex code that I...

Square root of 4.1-- do you have to use calculus? In order to solve square root of 4.1, is there a simple arithmetic method or do you have to use calculus and use that "tangent line approximation formula"? I wonder how do calculators do it... does anybody know?

does anyone know any specific method to find the square root of a polynomial like : 4x4 + 8x3 + 8x2 + 4x+ 1 ?? thanks in advance!

Homework Statement y'' -2y' +5y =0 , y(0)=1, y'(0)=1 you get a complex root conjugate. Homework Equations y=e^(rt) y'=re^(rt) y''=r^2 * e^(rt) The Attempt at a Solution I have in my notes sin(omega*t)e^(sigma *t), cos(omega *t)e^(sigma). I don't think i took down the notes...

Homework Statement If p is prime \sqrt{p} is prime. Are there flaws in my proof ? Homework Equations The Attempt at a Solution Assume \sqrt{p}=\frac{m}{n} and gcd(m,n)=1 p = \frac{m^{2}}{n^{2}} Since p is an integer n^{2}|m^{2} but gcd(m,n)=1 Therefore...

Homework Statement if n>1, prove that \sqrt[n]{n} irrational Homework Equations n/a The Attempt at a Solution so suppose it is rational, so i know \sqrt[n]{n} must be integer, say p then n=p^n and how do i prove this is not true?? i can prove if p>1 then p^n>n for all n>1 by induction...

Homework Statement Prove the following limit: lim_{n \rightarrow \infty } n^{ 1 / n } = 1 Homework Equations Not sure. The Attempt at a Solution Given any \epsilon > 0, choose N \in \mdseries N s.t. \left| n^{ 1 / n } - 1 \right| < \epsilon for all n > N I am not sure...