Radical Definition and 162 Threads

Here's a slight brainteaser for you all ! Seems simple at sight but can be harder than you think :D P.S I'm working on it as of now, it's an interesting question. Solve : 1/(√x+√(x+2))+1/(√x+√(x-2))=1/4

I'm trying to derive T= 2π√m/k to become k= 4π2m/T2 How is that happen? Can someone please explain it to me? Thanks in advance!

Homework Statement Need to do this integral as part of a problem \int \frac{xdx}{\sqrt{x^2+a^2-\sqrt{2}ax}} I can't think of any substitution that would work, or any way to factorize. I think this is a standard integral, but can't remember everyone so I just want to learn to solve it.

This may seem elementary, but it's been awhile since I've done heavy algebra work. I used the quadratic formula to get this equation: \mu = (\pm \sqrt{1 - 8x^{2}} - 1)/2 and I'm trying to simplify to: \mu = (\sqrt{1 + 8x^{2}} - 1)/2 If anyone could just point me to any resources that could...

Hi all I am an Mechanical Engineering major and I had a quick chemistry question. This may be crazy since I only had 2 semesters of College Chem If I had a tank of just bromine gas. Now my understanding is that these diatomic bonds can be broken by simply exposing the gas to sunlight. If...

Homework Statement Find the inverse of each of the following functions Homework Equations y= [sqrt] x^2 + 9 The Attempt at a Solution y = [sqrt] x^2 +9 x= [sqrt] y^2 +9 x-3= y I did the sqrt of 9, and sqrted y and its wrong. The answer is apparently y=+/(plusminus)...

Homework Statement f(t) = t^2- \sqrt{t} Find f'(t) Homework Equations Difference Quotient The Attempt at a Solution f(t) = t^2-\sqrt{t} \lim_{h\to0} \frac{(t+h)^2-\sqrt{t+h}-t^2+\sqrt{t}}{h} \lim_{h\to0} \frac{t^2+2th+h^2-\sqrt{t+h}-t^2+\sqrt{t}}{h} \lim_{h\to0}...

Homework Statement \frac{d}{dx} x+\sqrt{x} Using the definition of a derivative, no rules allowed. Homework EquationsThe Attempt at a Solution \frac{d}{dx} x+\sqrt{x} \lim_{h\to0} \frac{(x+h)+\sqrt{x+h}-x-\sqrt{x}}{h} \lim_{h\to0} \frac{(x+h)+\sqrt{x+h}-x-\sqrt{x}}{h} \lim_{h\to0}...

Hey, probably a stupid question but I can't seem to find an answer anywhere. Is a hydrogen free radical just a single hydrogen atom? A hydrogen atom has an unpaired electron bound right? Thanks in advance

sqrt(65/7)/[2sqrt(2)] I know how to simplfy radicals but this one has me stuck. I tried to answer it and i got sqrt(65)/[2*sqrt(2)] is this right?

PROBLEM 1: SOLVED THANKS TO POSTER DICK How can I prove these two field extensions are equal? Q(√3, -√3, i, -i) = Q(√3+i) where Q is the field of the rational numbers. I got Q(√3+i) ⊆ Q(√3, -√3, i, -i), that direction is easy: Let m ∈ Q(√3+i). Therefore, m = q + p(√3+i) where...

I am reading the beginning of the chapter about Conjugated Unsaturated Systems and it is discussing relative stability of the allylic radical in comparison with other compounds. This is what it tells me for the DH°: Allylic Radical - 369 kJ*mol-1 3° Radical - 400 kJ*mol-1 2° Radical - 413...

Homework Statement Evaluate the following limits: lim sqrt(x^2-3x+1)-x x->\infty lim sqrt(x^2-3x+1)-x x->-\infty 2. The attempt at a solution http://img816.imageshack.us/img816/9995/limitproblem11.jpg We have to enter in the answers online into a program that tells us if...

One form of the third law of thermodynamics states that ; in absolute zero temperature,entropy is absolute that means it does not depend on any of the properties of the system.the question is ; is this a radical feature for absolue zero or absolute zero is only a limit i.e. the dependence of...

tried to solve the problem with foil method but i got confuse can someone help 1) (-7 + \sqrt{3x})( 4+ \sqrt{3x}) -7 * 4 = -28 -7 * \sqrt{3x} = -7\sqrt{3x} \sqrt{3x} * 4 = 4\sqrt{3x} \sqrt{3x} * \sqrt{3x} - does this equal \sqrt{3x} square or is it just 3x or leave it \sqrt{3x} this is what...

anyone mind checking my homework and help me with the problems i got wrong 1)-5\sqrt{3} - 3\sqrt{3} = -8\sqrt{3} 2)2\sqrt{8} - \sqrt{8} = 4\sqrt{2} - 2\sqrt{2} = 2\sqrt{2} 3)-4\sqrt{6} - \sqrt{6} = -4\sqrt{6} 4)-3\sqrt{5} + 2\sqrt{5} = \sqrt{5} 5)-3\sqrt{27} - 3\sqrt{27} -...

I am studying a particular physicist/philosopher and his views regarding reality outside of sentient beings. The term idealism is introduced and defined in his definition of terms, but I am a little confused over one of his specific variants of idealism that he defines, namely radical idealism...

Homework Statement I got this expression while solving a problem. sin(theta)=[√3+1-√(4-2√3)]/4 Using calculator I got RHS=0.5 How do we simplify it without using a calc? Homework Equations The Attempt at a Solution

Hello, and thank you for any assistance offered. I believe the attached nested radical to converge to a value, but I can't find what it is. I've tried the typical recursive function methods to no luck.

Hello, I was wondering, if there is some good and easy to use computer programm, that, given a set of polynomials, tells me if they generate a radical ideal. Preferably as a Mathematica package.

A hydroxyl radical (O-H*) in the gas phase is found to be in a rotational state with a given wavefunction (Long wavefunction, not needed for my questions). Calculate the expected value of Lz (angular momentum in z) for the radical. Is this the right equation? Lz=mlħ ? In which orbital...

Problem: A hydroxyl radical in the gas phase is found to be in a rotational state with the wavefunction given, it's a long wavefunction so I'm not going to post unless needed. a) Calculate the expected value of Lz for this radical in SI units. I think Lz=mlħ is important for this...

Homework Statement I have to rewrite the following expression using a radical. I know the correct answer according to my textbook is 4x√x. Homework Equations 4x ^{3/2} The Attempt at a Solution √4x^3 is this the right start?

Homework Statement lim as h->0 of (f(x(sub 0)+h)-f(x(sub 0))/h f(x)=3\sqrt{x}+2 x(sub 0)=9 Homework Equations limit laws and factoring (my first post, not sure what I need to write here) The Attempt at a Solution =lim as h->0 of (f(9+h)-f(9)0/h =lim as h->0 of...

why would radical bromination of 2 methylbutane gives 1-bromo-3-methylbutane, 2-bromo-3-methylbutane, 3-bromo-3-methylbutane, and 1-bromo-2-methylbutane? i don't see any methyl shife in this reaction. Some one please help

Homework Statement The initiation step in chlorination of methane is as follows... http://upload.wikimedia.org/wikipedia/en/thumb/3/32/MethaneChlorinationMechanismInitiation.svg/260px-MethaneChlorinationMechanismInitiation.svg.png We get two chlorine radicals as a result. Next we have two...

Homework Statement (m3n/p)1/2 Homework Equations The Attempt at a Solution I believe it's multiplied by p1/2. Hurt me.

What are some techniques for integrating functions that are or contain radicals? I am familiar with trigonometric substitution. Are there any other "common" techniques or special functions that can be used to integrate these functions? or does trigonometric substitution basically take care of...

Homework Statement How do you expand a radical? Homework Equations The Attempt at a Solution

Homework Statement Find the horizontal asymptotes for the following equation: Homework Equations f(x) = \sqrt{x^2+4x}-\sqrt{x^2+x} The Attempt at a Solution First I factored f(x): f(x) = \sqrt{x}\sqrt{x+4}-\sqrt{x+1} Then I conjugated it: f(x) =...

Homework Statement 86300=\frac{86400}{1/\sqrt{1-(v/299000000){2}}} Homework Equations The Attempt at a Solution When I square each side I get an astronomicly high number.

Homework Statement There is no problem, ^title^, just a quick question :) The book's answer: \frac{x\sqrt{x}-x\sqrt{2}+2\sqrt{x}-2\sqrt{2}}{x-2}} My answer: \frac{x+2\sqrt{x}-x-2\sqrt{2}}{x+2} I combined like terms in the numerator... at least I think I did it correctly?

Evaluate if the following limit exists: lim_{x\rightarrow1}\frac{\sqrt[3]{x}-1}{x-1} My work: lim_{x\rightarrow1}\frac{\sqrt[3]{x^{2}}-1}{(x-1)(\sqrt[3]{x}+1)}} I did the conjugate, but I'm still left with a radical in the numerator, and I can't seem to factor any further. Can...

I am sure that it's a stupid question that has allready been answered in the past, but I couldn't find the solution anywhere. Well I want to know why the following attached equality is not true:

Homework Statement Sorry, I don't know latex yet! The problem: -4/9(x^9)[(3/x^2)-(1/(2^1/3))] when x = 2^1/6. I'll put it in words too, cause that looks confusing. Negative four-ninths x to the ninth, times three over x squared minus one over the cube root of two, when x equals the sixth root...

I want to find prime and jacobson radical radicals in Z[T]/(T^3), here Z = integers. Is it true that Z[T]/(T^3) is a field, because T^3 is irreducibel over Z[T]. If it is true that Z[T]/(T^3) is a field then 0 is the prime and jacobson radical radical. Is it true please help.

http://www.newscientist.com/channel/fundamentals/mg19826542.300-four-radical-routes-to-a-theory-of-everything.html The New Scientist 3 May 2008 issue cover story was about Four Radical Routes to a Theory of Everything, by Amanda Gefter. It would be interesting to know what the four...

Do you think that combating the free radical problem with aging could extend human lifespan beyond the mean lifespan if so how much do you think it could extend it do you think it couldn't extend it unless other problems relating to aging were dealt with as well? I know antioxidents have rarely...

From the book..." \sqrt[4]{(-4)^2}=\sqrt[4]{16}=2. It is incorrect to write \sqrt[4]{(-4)^2}=(-4)}^\frac{2}{4}=(-4)}^\frac{1}{2}=\sqrt{-4} ..." I understand the math involved but want to be sure of the exact reason why the first part is correct and the second is not. Is it because of the...

Could a tutor check my solution to my radical question? It is enclosed in this attachment as a word document.

I have to simplify this equation and express it as a radical at the end. 16x^7 / y^4 and cube root everything. I've tried expressing everything as exponents but it doesn't seem to get me to where i want to go. I attempted at factoring into two radicals with one containing a perfect...

I would love to know the definition of a radical number...JUST a radical number. I'm terrible at memorizing anything and have completely forgotton this term. I don't want any other inormation then what I am asking. All I want is a few sentences to explain a radical number. Equations are the easy...

With regard to examinations, is it true that radicals must typically be "reduced", if possible? For instance, with fractions, you would hardly ever leave 4/8 as it is, but instead reduce it to 1/2. Well let's say that durring an exam, you arrived at \displaystyle{\sqrt[3]{81}} for an...

decimal to radical algorithm? does anyone know if there is a method of writing a decimal number in its simplified radical form?? I really would like to know if there is

Homework Statement When heating the methyl methacrylate reaction (methyl methacrylate and dibenzoyl peroxide) to 90-95oC, why do bubbles evolve from the solution? Homework Equations None The Attempt at a Solution I'm not sure why the bubbles form. Any hints or helpful websites?

Homework Statement Write the expression in simplest radical form, if a radical appears in the denominator, rationalize the denominator Homework Equations \sqrt{9x^2-6x+1} The Attempt at a Solution the answer in the book says the answer is 3x - 1 I do not understand this...

I have a project in which I need to write a paper on how radical expressions are used in careers. I can think of plenty of careers that use radical expressions, the problem is, no matter how much I research I can't find anything on <i>how</i> they are used. I have tried to find mathematics of...

Homework Statement Let A be any ideal of a commutative ring with unity R. Show that the nil radical of A, N(A)= {r|r^n is in A} where n is a positive integer, and n depends on r. Homework Equations The Attempt at a Solution i don't quite understand the concept of the nil radical...

This isn't exactly homework, it was a question we had on a test and I had no idea at all of how to do it, although I think I did good on the other questions. The result that it came to, I can't remember exactly what it was, looked kind of like this: (2 root 3 + 3 root 4) over (-5) My...

Hey everyone, My class recently started radical numbers, and I haven't a clue on how you simplify them! Heres a few of my homework problems. if someone could possibly walk me through how you do them It would be greatly appreciated. http://img495.imageshack.us/img495/6903/math0oj.png...