Square root Definition and 378 Threads

Hi, I have a quick question about making quantum mechanics relativistic by simply replacing the hamiltonian by a relativistic hamiltonian. If we write the hamiltonian operator as: H = \sqrt{P2c2 + m2c4}, schrodinger's equation in position basis becomes: i\hbar\dot{\psi} =...

If I have a matrix valued function A(x) of some scalar x, how do I compute the derivative of the square root of A with respect to x? It seems like it should be simple, but I can't find it anywhere on the internet. Thanks!

Is the answer to sqrt -81y^3 : y sqrt-81y? or is there no real solutions? Also for this radical equation: sqrt 2n-5 - sqrt 3n+4=2 I worked it out and can't seem to get an answer. Is there no real solutions?

At first I thought that there is no square matrix whose square is the 0 matrix. But I found a counterexample to this. My counterexample is: \left( \begin{array}{cc} 0 & 0 \\ 0 & 1 \end{array} \right) However it appears that my counterexample has a 0 row. I'm curious, must a square root of...

Homework Statement Ok, working on a inverse function question, and I got stuck with something. Can someone explain the steps that makes this possible here. Something I am missing :( f(x) = √(x^3 + x^2 + x + 1) How is the inverse of the above function this... 3x^2 + 2x + 1 / 2√(x^3 + x^2 +...

Homework Statement I know how to prove that square root of 2 is irrational using the well ordering principle but what I'm wondering is, how can we use the well ordering principle to prove this when the square root of two isn't even a subset of the natural numbers? Doesn't the well ordering...

It can't be x, because you get a positive number when x is negative.

If you could see the image attached, I think it looks better than me typing it here. Didn't know how to embed the image. I would just like to know how it becomes 2v to √2v. EDIT: Ignore. Figured it out. Don't know why I was even baffled. :/

Provided is a function f(x)=\sum_{j=1}^n ||x-x_j||, for x being a two dimensional vector, where ||.|| denotes the Euclidean distance in 2D space. How could one obtain a derivative of such a function?

Hi. I just wondered why we use a 1/\sqrt{V} in the Fourier expansion of the vector potential. A regular 3 dimensional Fourier expansion is just f(\vec r) = \sum_{\vec k} c_\vec{k} e^{i \vec k \cdot \vec r} but as the solution to the equation (\frac{\partial ^2}{\partial t^2} -...

I have to find the limit as x→∞ of √(x2+x)-xI can't rearrange this into a form where I can put infinity into the expression and get a meaningful answer. I've tried taking out square roots to get √x( √(x+1)-√x ) but if I put infinity into this I just get ∞(∞-∞) which is meaningless. Now I know...

Homework Statement ∫(e^x)/(√4-e^(2x)) Homework Equations arcsin of x The Attempt at a Solution I know how the problem should be solved and have an idea of what the final answer will be. My only question is, how would I take out the four from the square root, in order to make it...

Homework Statement Find dy/dx when y=\sqrt{ln x} Homework Equations d/dx of ln x is equal to 1/x times d/dx of x. The Attempt at a Solution I tried to raise the ln x to the 1/2 power instead of keeping it under a square root sign, but I had no luck. I'm struggling with Calculus. I...

Its been a while since I have taken any kind of math class, I am a bit rusty in general algebra. Can someone explain how I would multiply an equation like this (2x-1)sqrtof x-3x is it just like normal distribution? Would I just put the answer underneath the square root? sqrt2x^2-6x^2-x+3x?

Homework Statement I have the function H^2 + 12756H and I want to find the domain and range of it's square root algebraically. Homework EquationsThe Attempt at a Solution I understand y= √(H^2 + 12756H) is undefined if H^2 + 12756H < 0, however I don't get how to find its domain and range...

Hi. I'm currently reading about (negative frequency) solutions to the Dirac equations which can be written on the form \Psi = ( \sqrt{p \cdot \sigma} \chi, \sqrt{p \cdot \bar{\sigma}} \chi)^T e^{-i p \cdot x}For any two component spinor Chi. But the dot product with the four vector p and the...

Finding Limit As "X" Approaches Infinite Of Square Root Function Homework Statement Homework Equations None that I am aware of. The Attempt at a Solution What I tried to do to solve this problem was first, multiplying the function by its conjugate, and then simplifying the...

Homework Statement The image has the question I don't quite understand! Homework Equations The Attempt at a Solution I understand how to get √(√2 - x) but I don't get how they end up with: 4√2 - x ?

Hoping someone can push me in the right direction with this one. Plume snookered. It's to simplify: 2√3(3+√3) Guessing first calculate (a^2 - b^2*c) in the square, though the 2 is throwing this an I'm not sure how the answer is 6√3 + 6, an not 18√3 ?

Homework Statement Prove Square Root of 15 is Irrational The Attempt at a Solution Here's what I have. I believe it's valid, but I want confirmation. As usual, for contradiction, assume 15.5=p/q, where p,q are coprime integers and q is non-zero. Thus, 15q2 = 5*3*q2 = p2...

IDK if this should be in the precalc section, but I was wondering how to reduce \sqrt{(3+\sqrt{5})} / \sqrt{(3-\sqrt{5})} to (\sqrt{5} + 1) /(\sqrt{5} - 1)

In what branches of mathematics is this proven.. I have never seen a proof, so I wonder if anyone can give me the basics of what is done to proove it or got a link to a proof.. Edit: By square root I mean the positive square root.

Suppose I have to solve for y: x\leq 1 (x - 1)^{2} = y So I know that (x - 1) will always be 0 or a negative, therefore I must take the negative square root of (x - 1): -\sqrt{(x - 1)^{2}} = -\sqrt{y} Am I to understand that this is the same as: -1 \cdot \sqrt{(x - 1)^{2}} = -1 \cdot...

Let $a,b \in \mathbb{Z}$, and if $a+b\sqrt{2}$ has a square root in $\mathbb{Q}(\sqrt{2})$, then the square root is actually in $\mathbb{Z}[\sqrt{2}]$. Only one approach comes to my mind. Let $r_1, r_2 \in \mathbb{Q}$ such that $a+b\sqrt{2}=(r_1+r_2\sqrt{2})^2$. This gives $a=r_1^2+2r_2^2...

I was playing trying to work through a proof in Apostol's Calculus and can't quite understand a step noted. This is from chapter 3, theorem 1.35. Every nonnegative real number has a unique nonnegative square root. The part where you are establishing the set S as nonempty so you can use LUB it...

Homework Statement If X^2=Sqrt(x1^2+x2^2+x3^2+...)=> X? and vice versa If X=x1+x2+x3+...=> X^2? Homework Equations The Attempt at a Solution

Years back i learned the digit-by-digit calcualtion of square root like this : http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Digit-by-digit_calculation But i don't know why this works. Wikipedia gives kind of an explanation but i don't understand it. How does this method work?

Homework Statement Integrate: sqrt(1/4 + t^2 + t^4)The Attempt at a Solution I'm really not sure on how to go about integrating this, it's actually integrate from -1 to 1, the solutions manual has a method I'm not familiar with. I thought of factorising it first, although doing that hasn't...

line integral -- confusion on squares and square root terms Homework Statement Do you see where they have sqrt(16 sin^2t etc = 5? How do they get that, the answer should be 7, the square root of 16 is 4, sin^2 + cos^2 is 1 and the square root of 9 is 3, 3 + 4 = 7. It's like they're...

By chance I stumbled on this "almost" equality: \frac{1}{5}(1/2+2/3+3/4+4/5+5/6+6/7+7/8+8/9+9/10) ≈ √2 - 7.2×10^{-6} I'm just wondering, are these funny coincidences simply, well, coincidences :biggrin: or is there some kind of explanation? I've see a ton of other funny stuff like...

I am trying to prove sqrt(3) is irrational. I figured I would do it the same way that sqrt(2) is irrational is proved: Assume sqrt(2)=p/q You square both sides. and you get p^2 is even, therefore p is even. Also q^2 is shown to be even along with q. This leads to a contradiction. However...

Is it possible to find √n using only the times table and the 4 operations?

Homework Statement Define f(x)=\sqrt{}(x + (\sqrt{}(x + \sqrt{}x) Determine where f is differentiable and compute the derivative Homework Equations f'(xo)= lim as x approaches xo (f(x) - f(xo))/(x - xo) The Attempt at a Solution By the definition, f(x) = \sqrt{}x does not have a...

Homework Statement The problem and solution are included. Homework Equations Double integration. The Attempt at a Solution Firstly, I'd like to mention that the additional ρ under the square root is there accidentally and that it should be outside of the square root such that it...

I'm having a little bit of trouble figuring out how exactly to do this. Prove that \sqrt{n+\sqrt{n+\sqrt{n+\sqrt{n+\sqrt{n+\cdots}}}}} = \frac{1\pm\sqrt{4n+1}}{2}. How exactly does one go about doing this? I mean, I understand it goes on infinitely, but doesn't that create an infinitely...

\lim_{x\to +\infty}\sqrt{x^2+3}-x sorry first of all how do you turn this string into latex I don't see the icon tool on the editor thnx

Homework Statement Let a be a positive real number. Prove that if a is irrational, then √a is irrational. Is the converse true? Homework Equations So, an irrational number is one in which m=q/p does not exist. I understand that part, but then trying to show that the square root of an...

Homework Statement Solve \sqrt{-e^{(i2\pi)/3}} Homework Equations The Attempt at a Solution I seem to be missing something simple, as I take: \sqrt{-1} = i then, e^{(1/2)*(i2\pi)/3} which comes out as: ie^{i\pi/3} however, the solution is: -ie^{i\pi/3}, and I can't seem to see where...

Homework Statement Simplify \sqrt {10 + \sqrt{24} + \sqrt{40}+\sqrt{60}} Homework Equations \sqrt{a+b+2\sqrt{ab}} = \sqrt{a}+\sqrt{b} The Attempt at a Solution \sqrt {10 + \sqrt{24} + \sqrt{40}+\sqrt{60}} = \sqrt {10 + 2 \sqrt{6} + 2 \sqrt{10}+ 2 \sqrt{15}} Stuck...

Homework Statement z = (n + i)^{2} n is a positive real number, and arg(z) = \frac{\pi}{3} Find the value of n. The attempt at a solution I am reviewing old problem sets from years past, and came across this problem that appears pretty simple. I have my old answer as n=\sqrt{3}...

why there is no answer when negative value is being square root? e.g: square root of -9 when i try to find answer from calculator, ''math error '' appears.. so is there an explanation for this question?? this question may looks so weird..but i m juz asking out of curiousity..

Can a kind person explain to me why I appear to have two conflicting solutions to: \int^{\frac{1}{\sqrt{2}}}_0dx\sqrt{1-x^2} Solution 1 : Standard trigonometric substitution: x=\sin\theta Integral becomes...

Please see attached. This is a general question for a more complex thermo problem, but it fits this form. Are there any tricks to getting expressions out of square roots in solving DEs? y=y(x) x=x(t) I want to get y by itself so I can integrate with respect to x, but it is trapped in a...

How in the world do you take the square root of a matrix in Mathematica? All the ways I've tried haven't worked... Thanks!

Homework Statement What I am confused about is: x - \sqrt{2}=0 x=\sqrt{2} is it equal to x=\pm\sqrt{2} ? Homework Equations The Attempt at a Solution The way I know it, those two are not equal. But my teacher insists on saying that whenever there is a square root, we should always...

Homework Statement Let f be a quadratic polynomial function of z with two different roots z_1 and z_2. Given that a branch z of the square root of f exists in a domain D, demonstrate that neither z_1 nor z_2 can belong to D. If f had a double root, would the analogous statement be true?Homework...

Homework Statement Let A be the matrix: -5 -3 18 10 Find an invertible matrix X so that XAX-1 is diagonal. Use this to find a square root of the matrix A. Homework Equations DetA - xI (A-\lambdaI)v = 0 The Attempt at a Solution So, I found DetA- xI, which...

In Ramakrishna's paper, http://arxiv.org/ftp/arxiv/papers/1111/1111.1922.pdf , he derived equation (9), page 5. It is a difference of two square-roots using an approximation method. Can anyone help in how this is done? Thanks

Homework Statement Does the principal branch square root of z have a Laurent series expansion in the domain C-{0}? The Attempt at a Solution Well I'm not really sure what a principal branch is? I believe that there is a Laurent series expansion for z^(1/2) in C-{0} because originally our...

Homework Statement Hello. I'm trying to solve this equation: 16.9038=\sqrt{1470tan\theta} Homework Equations The Attempt at a Solution I just need to know what theta is. It's been a while since I've calculated something like this and just need someone to show me the steps...