Radicals Definition and 103 Threads

Homework Statement Evaluate the limit of each indeterminate quotient: lim (x-->4) [2-(x^1/2)]/[3-(2x+1)^1/2] Homework Equations The Attempt at a Solution The answer in the book is 3/4. This MAY be wrong though. My attempt: I basically tried rationalizing the numerator AND denominator but...

±\sqrt { { x }^{ 2 } } \\ =±|x|\\ =±±x Wouldn't a plus sign or a minus sign be sufficient?

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?

Hi, Is there a general algebraic expression for the sum of a function inside a radical? I mean for something like this? \sum^{n}_{i=1}\sqrt{f(i)} The specific case is given with constant c: \sum^{n}_{i=1}\sqrt{c^4i^4+c^2i^2+1} And I supposed a related question is that, is there some way of...

Solve for: √(x-7) / √(x) -2 = √2 My attempt at a solution: I solved for x and it comes out to: 0 = x^2 - 64x +225 and then i plugged it into the quadratic formula: [-(-64)±√((64)^2-4(1)(225))]/2 and my answer comes out to be: 32±√799 although the answer on the back of...

Homework Statement I have a sequence an+1=sqrt(2+an) ,with a0 = sqrt(2) which leades to nested radicals. I am asked to show that for n approaching infinity: 1) the sequence converges to 2, and that 2) lim {(an+1 -2) / (an -2)} = 1/4 The Attempt at a Solution 1)I have proven the...

I am not too familiar with differential equations but am familiar with basic calculus, I came across this equation trying to describe a particular function: dy/dx =((sqrt((y-x)^2+y^2)-abs(y))/(y-x))*abs(y)/y Anyway I tried to separate the variables unsuccessfully and using v(x)=y(x)/x with...

I've been having trouble figuring out how to find the derivative of f(x) = x + √x The farthest I got was: [(x+h) + √(x+h) - (x+√x)]/h = [h + √(x+h) - √x] / h I got stuck here because I'm not sure how to cancel out h in numerator and denominator (if i can even do that at this stage)...

I managed to get the other problems right, but this one I've been fiddling with and can't seem to get the right answer. Homework Statement \sqrt {3b -2} - \sqrt {2b + 5} = 1 Answer: 22 Homework Equations -- The Attempt at a Solution For this I tried the method of...

More fun with radicals! ...As for the problem, I tend to get problems with this same form (but with slight differences such as two separate binomials underneath individual square roots) wrong. I'm not quite sure what I'm doing wrong, so I was hoping for some help. :D Homework Statement...

Homework Statement order 3 radical from (9+4radical5) + order 3 radical from (9-4radical5) *note: 9+4radical5 is all under the big order 3 radical. (so is the other one) Homework Equations in case you don't understand what i wrote (sorry, my language is not english and math linguistics...

Homework Statement log2√xHomework Equations The Attempt at a Solution I thought that it might be something like log2x - log2x but that's not right. The book examples don't have any radicals.

Homework Statement Simplify. \sqrt[3]{\frac{5}{4}} The answer according to the textbook is: \frac{\sqrt [3]{10}}{2} Homework Equations -- The Attempt at a Solution Separated numerator and deonominator into individual cube roots and multiplied both by \sqrt[3] {4} ...

As the title suggests, we know from the Abel-Rufini theorem that 5th order equations cannot be solved using radicals. I haven't managed however to find an either positive or negative answer to the following statement: "Can 5th order equations be analytically solved by means other than...

Homework Statement The expression can be simplified. Simplify the following...Homework Equations 1 _____________ - Starting equation √3 + √2 - √5The Attempt at a Solution 1 * [(√3 + √2) + √5] _____________...

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

We can see that if u=\sqrt{x+\sqrt{x+\sqrt{x+\dots}}} then u^2=x+u so u^2-u-x=0 This has solution \left( u-\frac{1}{2} \right)^2 -\frac{1}{4}-x=0 \Rightarrow u=\frac{1}{2} \pm \sqrt{x + \frac{1}{4}} This means that u \in \mathbb{R} \forall x \geq \frac{1}{4} In other words...

Homework Statement This is supposed to be really easy, but I don't think my answer is good Consider this \sqrt{1 + \sqrt{1 + \sqrt{1 + ...}}} I was hinted that a_{n + 1} = \sqrt{1 + a_n} for all n ≥ 0 and I am supposed to show that the sequence convergees The Attempt at a...

I have attached an image of my question because it was a bit difficult to type. Now, my question is : What is it's value upto infinity ?

Hello and good evening! I'm having a fair bit of difficulty with this question, any help would be appreciated. Homework Statement √(x2/2+11)=x-1 Answers are required in mixed radical form. Homework Equations The quadratic formula/factoring will be useful near the end of the problem...

Homework Statement Limit as h approaches 0 for [rad(5+h)-rad(5-h)]/h Homework Equations The Attempt at a Solution limit as h approaches 0 for [(5+h)-(5-h)]/h[rad(5+h)+rad(5-h)] limit as h approaches 0 for 2h/h[rad(5+h)+rad(5-h)] limit as h approaches 0 for h/[rad(5+h)+rad(5-h)] This...

Homework Statement This is the problem. I seem to be having a hard time removing the radicals. The answer should be 12/5. I have no idea how to get there. I am just trying to learn how to handle a situation like this, so I can be prepared in the future. 2x*(4x-1)^-1/2 - 3sqrt(4-x) = 0...

Homework Statement f(x)= 1/(5x2 +3) g(x)=1/(x-2)1/2 find (f+g)(x)The Attempt at a Solution for (f+g)(x) I use the common denominator by multiplying each side by (x-2)1/2/(x-2)1/2 and (5x2 +3/5x2 +3) respectively. I end up with a whole mess that I am unable to rearrange into anything useful...

Homework Statement (-3/x^(1/2)) / ((2/y^(1/2))-8) which, from my book, I see can be rewritten with radicals as: (-3/sqrt(x)) / ((2-8sqrt(y))/(sqrt(y)))The Attempt at a Solution Now, what I don't understand is how the denominator was rewritten. I understand that in the numerator, the 1/(...

Homework Statement Find the interval of convergence: \sum _{n=1}^{\infty } \frac{(-1)^n (x+2)^n}{3^n\sqrt{n}} Homework Equations The Attempt at a Solution \lim_{n\to \infty } |\frac{(x+2)^{n+1}}{3^{n+1}\sqrt{n+1}}*\frac{3^n\sqrt{n}}{(x+2)^n}| = \lim_{n\to \infty }...

Homework Statement Find the following limit: \lim_{x \to \infty} \frac{2+\sqrt{(6x)}}{-2+\sqrt{(3x)}} Homework Equations n/aThe Attempt at a Solution I know this shouldn't be that hard, but somehow I keep getting stuck on simplifying the equation. I think the first step is to multiply both...

im not sure if I am doing these questions correctly can someone check it 1) -3\sqrt[6]{3} - 2\sqrt[3]{192} - \sqrt[6]{320} -3\sqrt[6]{3} = -3\sqrt[6]{3} 2\sqrt[3]{192} = 6\sqrt[6]{3} \sqrt[6]{320} = 2\sqrt[6]{5} 3\sqrt[6]{3} + 6\sqrt[6]{3} + 2\sqrt[6]{5} = 3\sqrt[6]{3} -...

Homework Statement sqrt(7 + 2sqrt(6)) - sqrt(7 - 2sqrt(6)) Homework Equations The Attempt at a Solution In order to work out the radicals, I define the answer as "x". Now I can square both sides to get rid of some of the first radicals: sqrt(7 + 2sqrt(6)) - sqrt(7 - 2sqrt(6)) = x (sqrt(7 +...

Is it because they are unsaturated and can unfold. I understand how one radical would create another radical but I don't know exactly how radical could spread in a fatty acid chain. Any diagram would be useful. Thank you :smile:

Homework Statement 2 h(x)=∫√(1+t^3) dt find h'(2) x^2 Homework Equations The Attempt at a Solution I started out solving this equation by flipping x^2 and 2 and making the integral negative. From here on out, I'm lost. I've tried substituting u in for 1+t^3 and solving...

Homework Statement It's been a while since I've done derivatives. I'm working on a physics problem and can't seem to get the correct derivate for a function of the following form: f(x)= A [1+9x^2(x-4)^2]^1/2 A is a constant. The Attempt at a Solution I've tried various ways of...

Homework Statement (square root of 3 + square root of 5)(square root of 3-square root of6) Homework Equations The Attempt at a Solution Im confused on what to multiply what with.

Please help me understand further. I have attached a file using microsoft equation. I have try everything to include a square symbol and cube root symbol using the options here with no luck. I really need help with this problem. Please if you know how to include these symbol in this actual...

Even in my second semester of calc I have yet to see a situation where the extra step made any sense why is it important to write \frac{3\sqrt{13}}{13} instead of leaving \frac{3}{\sqrt{13}}. Its not a big deal but even my profs say its not that important so it has peaked my curiosity.

Homework Statement -60/120 ^1/3 Homework Equations I've gone through my book, and I'm supposed to find a number that when multiplied by a perfect cube I can bring it out and then cancel with the division. Try as I might with my calculator, I can't find one. Am I doing this wrong?The Attempt...

Homework Statement find the exact value of cos105 deg Homework Equations n/a The Attempt at a Solution i know up to cos(45+60)= cos45cos60-sin45sin60 i get lost with the converstions to radical numbers, for example sgrt(2/2) or sqrt2. how do i convert into radicals, and how...

I understand that the square root of (for example)j^16 is j^8. But when you have an odd squared root, like the square root of j^19, would it be j^9square root of j? Another quick question 12 radical 36 would be 72? Sorry, I know this is basic algebra, but I really have forgotten how to do...

I been trying to solve some nested radicals. I've been able to do: \[\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\cdots}}}}\] Which is pretty cool since it equals to the "Golden Ratio" or \[\frac{\sqrt{5}+1}{2}\] But I can't seem to do the following: \[\sqrt{1+\sqrt{2+\sqrt{3+\sqrt{4+\cdots}}}}\] Using a...

is there a way to express any given root of an integer in a continued fraction? i.e. Sqrt[2] = 1 + 1/(2 + Sqrt[2] - 1) and the process can be continued infinitely to get a fraction that defines the radical with only integers. so my question is can this kind of thing be done with any square...

Need Help With Radicals! can anybody help me with radicals, and how do you type a radical problem on the computer? because there's no radical sign on the keyboard

Hello. I wrote a simple program that helps me simplify radicals: #include <iostream> #include <math.h> typedef struct { unsigned int x, y; }pair; bool breakcube(unsigned int radi, unsigned short inx, pair& pr) { unsigned int cb = 0; for (unsigned int i = 2; i < radi; i++) { cb=i...

I am weak in this topic but I am certain that the following is has a solution in integers A,B,C,D. Find A,B,C and D as integers such that (3*2^{.75} + 7*2^{.50} + 7*2^{.25} + 7)*(A*2^{.75} + B*2^{.50} + C*2^{.25} + D) = 2047*(2^{.75} + 2^{.50} +2^{.25} + 1) . I deduced this by...

Homework Statement Homework Equations Basic rules- Power, product, and quotient The Attempt at a Solution The first step would be to rewrite the equation: f(x)= x^2/3 + 1/ x^1/2 I'm lost here. I don't know what to do when the variable is in the denominator like that...

Do radicals always have a +/- sign in front of them? For example the equation: y=\sqrt{x} Is that only a half of a sleeping parabola or is it a full one? Does a radical only have a +/- sign in front of it when it takes this form?: y^{2}=x \rightarrow y=\pm \sqrt{x} So, is...

I read somewhere that you are supposed to leave radicals in the denominator when dealing with calculus. Before, I used to rationalize them to the numerator but my Calculus book now has the answers written unrationalized. So I'm wondering if I should start getting use to NOT rationalizing...

how would I take the cube root of the square root of 2 as an exponential equation? the square root of 2 is 21/2 but I don't know what to do with the cube root.

Homework Statement This question is concerning a limit question. I have no problems finding limits but i need to be able to factor this equation. I need to be able to some how get rid of the (x-1) (x^(1/6)-1)/(x-1) The Attempt at a Solution I ust keep ending up in a loop geting a...

I missed the lectures for this topic, so I don't have the notes, so I was wondering if anyone could give me the idea behind how to solve quartics in radicals. I know its long and messy, so just the basic idea would do. For example: x4 + 2x³ + 3x² + 4x + 5 = 0 I recall something about...

Started this today and I'm okay with simplifying radicals that don't include variables, but I'm having trouble solving ones with variables, like \sqrt{49y^{12}. I can't decide if I have to root it out like this \sqrt{7y^{6} times \sqrt{7y^{6} or just root it out the way it is since it is in...

8^2/3 (9^1/2) <---- times (multiply) evaluate. THANKSS