Square root Definition and 378 Threads

Homework Statement find the square root of: 4+4(sqrt3)i put the answer in a+bi form Homework Equations finding the nth roots: √(r(cos(theta)+isin(theta)))=√r(cos(theta+2(pi)(k)/(n))+isin(theta+2(pi)(k)/(n) where k=0,1 The Attempt at a Solution first i converted my...

My notes claim that the square root loop \sigma : S^1 \longrightarrow RP^1 ; z=\cos 2\pi t +i\sin 2\pi t \longrightarrow [\cos \pi t, \sin \pi t] is a homeomorphism, where [x,y] is an equivalence class given by the antipodal equivalence relation on the circle. However, this map doesn't even...

Question is pretty simple : How do I know that square root 3/2 = 0.8660 or how can 0.8660 be converted into square root 3/2 more importantly. My calculator is out of style so it displays only numbers. Thanks

Homework Statement The matrix C is self-adjoint and positive definite on \mathbb{ C}^2. Determine \sqrt{\mathbb{C}} \in \mathbb{ C}^{2x2} . C=\left(\begin{array}{cc}5&-4i\\4i&5\end{array}\right) The Attempt at a Solution Characteristic polynomial: (5-\lambda)^2 - 16 = 0 What I...

I have no idea how to go about this, except that we are supposed to use proof by contradiction to show that the square root of 3 is an irrational number. Any help or tips is appreciated. Thanks.

Homework Statement solve for x: [ x / sqrt(x^2 + h^2) ] = [ d / sqrt(d^2 + h^2) ] I need to solve for x. Homework Equations sq rt * sq rt = what is inside the square root square both sides of an equation The Attempt at a Solution Can anyone help me remember how to get...

I've struggled for days reading about square roots of complex numbers and I get most of the problems but not this one. I really want to understand what is going on in this problem, hope someone can help! 1. The complex number (C) is C = 1/\sqrt{i*x} . find the two roots of C. The solution...

Homework Statement Maclaurin series for square root (1+x) Homework Equations The Attempt at a Solution I attempted to find the maclaurin series for the function Square root of 1+x. F(0)=1 first term= 1 F'(0)=1/2 second term= (1/2)x F''(0)=-1/4 Third term (-1/4)x^2...

hi there, I'm trying to plot r against \phi by solving the following ODEs using runge-kutta. The problem I'm having is with the square root. How do I know when it will be positive and when it will be negative? If this is a simple question I apologise I'm not that great with the maths :). E and...

Consider square root of 4. Can square root of 4 be +2 or -2? I asked that to my math teacher so he said: NO, square root of 4 is +2! But I can't really understand why it cannot be -2 since -2 squared is also 4. One thing I've imagined is: square root of 4 can be +2 or -2, but for...

hi there, i have written a small program in C++ and if the user puts in the wrong values for some of the variables the operation will end up trying to square root a negative number and this returns that the answer is not a number can anyone show me how to write an if function that if...

1. Homework Statement [/b] i have this thing: 2u\sqrt{}um is this expression the same as: 2u^3/2*m^1/2 Homework Equations The Attempt at a Solution

Homework Statement Find the linerization of square root of sin(2x) Homework Equations The Attempt at a Solution I don't even know how to start. What is linearization? Thanks

Homework Statement http://img37.imageshack.us/img37/1237/63391287.jpg Homework Equations $\displaystyle \Large \int udv$ = uv - $\displaystyle \Large \int vdu$The Attempt at a Solution can i take this 3 out of the integral as well and make it 3/8 *$\displaystyle \Large \int _0^8 sqrt(64 +...

Homework Statement why is it possible to take the cube root of a negative number and not a square root of a negative number? Homework Equations The Attempt at a Solution

Homework Statement (x-7)^2=(x+3)^2 2. The attempt at a solution I squared both sides and received x-7=x+3 However, that cannot be correct because the variables cancel out which means there is no solution. The book shows that there is a solution of 2

Homework Statement Find the Integral of \sqrt{sin(x)} Homework Equations none The Attempt at a Solution People say it's -2/3cos(x)^{3/2} which I don't think so or is it? thank you

Problem Calculating a limit with a square root, I'm stuck :( Homework Statement The limit is equation 9-t / 3-sqrt(t) as t approaches 9 I'm stuck on the how to simplify this? Thanks for any help. Homework Equations The Attempt at a Solution

Homework Statement show that \sqrt{1+ja} is equivalent to \pm(1+j)(a/2)^{1/2} with a>>1 Homework Equations Euler's formula? The Attempt at a Solution with a>>1 |z| = \sqrt{(1 + a^{2})} == a lim a-->infinity arctan (a/1) == \pi/2 \sqrt{z} = \sqrt{(ae^{j\pi/2})} \sqrt{z} =...

Homework Statement Hi again all, I've just managed to prove the existence (non-constructively) of a 'square root function' f on some open epsilon-ball about the identity matrix 'I' such that [f(A)]^2=A\qquad \forall\, A \,\text{ s.t.}\, \|I-A\|<\epsilon within Mn, the space of n*n matrices...

Could someone help me with this? I feel it should likely be easy, but I'm baffled anyway: Homework Statement Prove the validity of the limit lim x -> x_0 sqrt(x) = sqrt(x_0) Homework Equations use definition of limitThe Attempt at a Solution Generally confused. I start with |sqrtx - sqrtx0|...

Does anyone know how to solve for x in the following equation: x + \sqrt{x} = 6 I don't know how to solve for x with eq'ns like this, and I'm studying inverse fxns right now, so I'm told that's what I'm supposed to do. The square root sign is throwing me off. The first time I tried...

Hello, I was just wondering if there is a special notation for a principal square root... I suppose using absolute value would work.. \left|\sqrt{9}\right|=+3 But it doesn't seem as fitting as an actual special square root symbol. Maybe something like this? \sqrt[+]{9}=+3 Also...

Homework Statement I wonder how to deal with the square root of Dirac Delta function, \sqrt{\delta(x)}. Actually, this comes from a problem which asking readers to calculate the wave function of a free particle and of a harmonic oscillator at time t, provided that the wave function at time...

I know that if n is odd and has k distinct prime factors, then the number of roots, x^2 = 1 (mod n), is equal to 2^k. However, I don't know how to give a formal proof to it. I simply want to bypass the generalized form x^2 = a (mod n). How can I prove it directly? Thank you.

Hello! I got the following exercise: \frac{lim}{x\rightarrow6-} {\sqrt{3x-18}} Now, since I need to evaluate the limit from the function coming from the left to the right that means that I can evaluate the function using x as a value very close to 6, but not six, right? So, since I would...

Homework Statement given the sequence {a_n} converges to A (non zero), show sqrt(a_n) = sqrt(A) Homework Equations The Attempt at a Solution I've tried to expand |sqrt(a_n) - sqrt(A)| as |a_n - A|\|sqrt(a_n) + sqrt(A)| since that gives me the numerator to work with, but I can't...

Homework Statement My prof showed us the proof that sqrt2 is not a rational number. She said, however, that we haven't proved that it is irrational, because we haven't proved that sqrt2 exists. How would we go about proving this? Homework Equations N/A The Attempt at a Solution...

Homework Statement Can someone advice me how to solve this square root equation? n_{0}=1.5*10^{15}+\sqrt{(1.5*10^{15})^{2}+[(0.05)n_{0}]^{2}} The answer should be n0=3.0075*1015 I can't figure out how to open up the square root to solve the equation for n0. Stuck here staring at the...

Homework Statement x^2 - 1/2x - 3/16 = 0 The Attempt at a Solution Actually, I don't know where to start since I have fractions.

I am looking at the derivation for an expression that relates the concentration of an oxide to time. It appears that to do this, the author takes the limit of sqrt(A+Bt), where A and B are constants as t approaches zero and infinity. Is there an easy way to do this without making assumptions...

Homework Statement (x - 1)^2 = 4 The Attempt at a Solution This is what I've done (x - 1)^2 = 4 Everything inside parenthesis goes to: ^2 x^2 - 1^2 = 4 now we got x^2 - 1 = 4 Now (I think) I use the square root method x^2 - 1 = √4 x^2 - 1 = 2 Now I factorize: (x - 1) (x +1) = 2 This is...

Homework Statement Given f(x) = -x2 - 2x + 3, x < -1 Find f-1. Find f-1f. Homework Equations Nil. The Attempt at a Solution Actually I worked out much of the question already, and I already know that f-1f: x -> x. The problem is, I can't seem to get f-1f(x) = x on...

Homework Statement What is f'(x) of f(x) 1/sqrt(2x)? 2. The attempt at a solution In applying the problem to the derivative formula: (1 / sqrt(2(x + h)) - 1 / sqrt(2x)) / h I multiplied the problem by a special form of one but that only put the rationals on the bottom of the...

Homework Statement Can someone explain to me how |-4|= \sqrt{(-4)^{2}} I'm wondering why you can't cancel out the square root sign and the square above the -4, to leave you with -4. The Attempt at a Solution I know this has something to do with the absolute value of -4, being 4, but...

The other day I was playing with my calculator and noticed that \sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+...}}}} \approx 2 But, what is that kind of expression called? How does one justify that limit? And, to what number exactly does converge, for example...

1.I can't figure out how the \sqrt{1+((x^2)/(4-x^2))} simplifies to 2 times\sqrt{1/(4-x^2)} I have tried rewriting it in different ways, but I can't see how it simplifies. \sqrt{x^2 + 1/4-x^2}

(1- sqrt 3i) ^3 I am having trouble solving the sqrt 3i part. I think I need to use de moivres theorem but I am unsure. If someone could push me in the right direction that would be a massive help. Thanks.

Hi, We use as an integration form in Riemannian geometry the covariant \int \sqrt{g}d\Omega I understand how this is invariant under an arbitrary change of coordinates (both Jacobian and metric square root transformation coefficient will cancel each other), what I don't understand is why don't...

this is a strange problem easy to solve but I am having trouble understanding it intuitivly. Assume we choose a location point and name it 0. Next, in arbitrary direction and distance we place the number 1. Hence, we have created a scale(number line) that extends as much as we like. Now we...

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...

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...

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.

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...

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...

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...

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...

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

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...

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...