Root Definition and 918 Threads

Express each term of the sequence \{\sqrt{2}, \sqrt{2\sqrt{2}}, \sqrt{2\sqrt{2\sqrt{2}}}, ...\} as a power of 2. I found \{2^{\frac{1}{2}}, 2^{\frac{3}{4}}, 2^{\frac{7}{8}}, ...\} but I can't get the formula for it so I can find it's limit.

I am taking calc 2 and I think we just finished up all the different ways of integrating, yet I can't figure this seemingly very simple one out. Any help is greatly appriciated.o:) \int\sqrt\frac{1}{x}dx

Hey-- I'm writing up a physics lab report on centripetal force; at the moment I've hit a problem with the velocity squared vs. radius graph. The graph *should* show a root curve (v^2 = Fr/m) but all of the regression utilities I've used churn out an exponential curve. Here are the four points...

hey guys on my textbook, it says that square root of 4 equals to 2 but not negative 2. The book is wrong right?

does anybody knows what does the eqn such as sqr root of (x-4)^2 + y^2 use to find for?? pls help...

why is the square root of 25 just 5 but when the question x^2 = 25, the answer becomes +/- 5? whats the logic here? i don't quite get it. thanks.

suppose you have square root of -16 times square root of -25 (in separate square root symbols). would the answer be: a) no solution - can't have negative square roots b) 4i times 5i which equals 20i^2 which is -20 c) -16 times -25 which is +400, then the square root of that is 20...

I hold that the "root of all evil" (for humans) is when a human uses another human as a means to an end, even if those being used agree. Comments -- other roots for the tree of evil ?

It is rather well known that the color of flowers on Hydrangea depends upon the pH of the soil in which it is planted. Low pH in the soil means blue flowers and high pH means pink. Here is a quote from the Texas A&M site on Hydrangea: Sometimes a single plant may have shades of both pink and...

I want to find a nice and elegant proof of the Rational Root theorem, but I get stuck. I read some stuff on the Internet, but I have not found a complete proof of the theorem. Here's my try: Say we have a polynomial: F(x) = \sum ^{n}_{r = 0} a_{n}x^{n} = a_{n}x^{n} + a_{n - 1}x^{n-1} +...

The determinate of the following 3x3 matrix 1-y, 2 , 3 2 , 4-y, 5 3 , 5 , 7-y gives a cubic that simplifies to, y^3 - 12*y^2 + y + 1 = 0. Now, apparently the teacher picked random numbers for the original matrix, making the problem delve into other realms of mathematics...

Find all real/imaginary roots to x^9=16x

Please help with these simple questions just not understanding it properly. Find square root, of -6i let sqroot of -6i= x+ yi then -6i=x^2 - y^2 +2xyi x^2 - y^2 = 0 and 2xy=-6 then xy=-3 x=-3/y and then solve simu.. i got y= 3 and x=-1 y=-3 x=1 so the anser is +_(-1+3i) BUt that...

Quote: Originally Posted by Artermis Hello Moonbear, I don't know if you know me but I'm a relatively new member but I know that you are very knowledgeable and helpful, hopefully you'll be willing to help me with this. Hi, I've seen you in the biology forum recently. Glad to have you...

I'm trying to program my 83 for Reimann sums and I believe I've got it now but to plug in for Y1= \sqrt{1+sin^3} how do I make the \sin^3 part because the parenthesis keep me from getting the ^3. I've tried the MATH button but it won't work that way.

I saw a proof saying the root of a prime is always irrational, and it went something like this: sqrt(r) = p/q where p/q is reduced r = p^2/q^2 r*q^2 = p^2 therefore, r divides p so define p = c*r r*q^2 = (c*r)^2 = c^2*r^2 q^2 = c^2*r therefore, r divides q also since r divides p...

This is Algebra 2 question... I have to prove that the square root of 2 is irrational... First we must assume that sqrt (2) = a/b I never took geometry and i don't know proofs... Please help me. Thank you.

I'm just wondering about something, look at this: \[ \begin{array}{l} \sqrt {3 + x} + \sqrt {2 - x} = 3 \\ \left( {\sqrt {3 + x} } \right)^2 + \left( {\sqrt {2 - x} } \right)^2 = 3^2 \\ 3 + x + 2 - x = 9 \\ 5 = 9 \\ \end{array} \] Obviously something isn't right...

An old man gives you a set square (http://www.buchhandlung-umbach.de/pbs/geodreick.gif ) and then asks you to draw a line of exactly the length \sqrt{3} . How would you do it?

cos(x)+cos(ix)+cos(x*i^3/2)+cos(x*i^1/2)=0 for x I have spent a lot of time finding an analytic root to this equation without success. An analytic root may not exist. I don't know. It is roughly equal to (8facorial)^(1/8)

Need to find the derivative of: f(t) = square root of 3t+2 / 4t-3 please help.

How do I show that 2 has no rational roots?

Start Windows Explorer, right-click the computer's root hard disk, and then click Properties how do I find the computer's root hard disk in order to righ click on it?

Square root of 2... Is it actually possible to produce a right angled triangle with sides exactly equal to 1m and 1m? Because this would produce a hypotenuse with length "square root of 2" m, which has no exact length. Thanks in advance. :smile:

Square root of -1... We say that the square root of -1 is equal to i ( or j ), and that this is therefore not a real number - but what is this fact actually useful for? Why over complecate things with something not on the number line - why is it so useful to treat the square root of -1 as a...

How do I find the derivative of f(x)=(square root x^2-2x)^3-9(square rootx^2-2x)

Hi, I'm trying to find this integral: \int \frac{x}{(x+1)\sqrt{1-x^2}}\ dx Because 1-x^2 has two different real solutions, I can write \sqrt{ax^2 + bx + c} = \sqrt{-a}(x_2 - x)\sqrt{\frac{x-x_1}{x_2 - x}} so \sqrt{1-x^2} = (-1 - x)\sqrt{\frac{x - 1}{-1 - x}} = (-1 -...

Show that the equation: 2x - 1 - \sin x = 0 has exactly one real root. \frac{d}{dx} (2x - 1 - \sin x) = 2 - \cos x = 0 2 = \cos x x = \cos^{-1} 2 Is there a better way to approach the root? any suggestions?

\begin{array}{c} {{A_n}={\sqrt{\sum _{z=1}^{n}{z^2}}} } \\ {{A_1}=1 } \\ {{A_{24}}=70}\end{array}\ Is there a proof that only for n =1 or n=24 that An is an integer quantity?

hi i was trying to determine the sqrt of -1,and here is wat i have done. sqrt of -1=-1^2/4,this further gives [[-1]^2]^1/4, which further gives 1^1/4 therefore the sqrt of -1 is 1^1/4 which is 1 have u any objections,let me know

Does i, the imaginary number, have a square root? This was bothering me for a while, then I thought I happened upon a simple solution, but have since forgetten. \sqrt{i}=?

Hi, A cubic equation has at least one real root. Can someone help me to prove this? Thx! LMA

Short root sequence question For the recursive sequence R_n = x + \sqrt {x - \sqrt {R_{n - 2} } } R_0 = x = k^2 - k + 1 \forall k \in \mathbb{N},\;k > 1 why does \mathop {\lim }\limits_{n \to \infty } R_n = k^2 ??

I don't get the use of imaginary numbers. To find the square root of negative numbers but it does not exist and it is not a real number. Can u please explain it to me.

Is there any law for finding the root of a complex number in catesian coordinates? without changing to polar, I've created 1, i just want to know is it worthy or not, so ... everybody who reads the message, please post the ROOT OF A COMPLEX NUMBER IN CARTESIAN COORDINATES LAW and let me...

A problem in my textbook guides you through this proof using a multiple integral. I follow the whole thing except for one step. It requires that you show that (sorry don't know latex, I(a,b) will denote integral from a to b, e the exponential) [I(-x,x)e^(-u^2)du]^2=I(R)e^(-u^2-v^2)dudv...

Why is it that the square root of x^9 for some x isn't always the same as x^(4,5) ? I tried to do this with x=12 on my TI-89 and it comes very close, the difference comes after like the 8th decimal or something, but shouldn't it be excactly the same?

Simplify 1/2[Loga N - Loga (N - 1)] I get something like 1/2[Loga N / (N-1)] Loga root[ N / ( N-1 ) Loga root [ (N * ( N + 1)) / N^2 - 1 ]

I need to show that this is an algebraic number. In other words, I need to show: an*x^n + an1*x^(n-1) + ... + a1 * x^1 + a0 * x^0 = where the a terms are not ALL 0 but some of them can be. Like for root 2 by itself, I have 1 * (root 2) ^ 2 + 0 * (root 2)^1 + -2 * (root 2) ^ 0...

I need to show that this is an algebraic number. In other words, I need to show: an*x^n + an1*x^(n-1) + ... + a1 * x^1 + a0 * x^0 = where the a terms are not ALL 0 but some of them can be. Like for root 2 by itself, I have 1 * (root 2) ^ 2 + 0 * (root 2)^1 + -2 * (root 2) ^ 0...

I need to show that this is an algebraic number. In other words, I need to show: an*x^n + an1*x^(n-1) + ... + a1 * x^1 + a0 * x^0 = where the a terms are not ALL 0 but some of them can be. Like for root 2 by itself, I have 1 * (root 2) ^ 2 + 0 * (root 2)^1 + -2 * (root 2) ^ 0

I saw this proof in class today to prove the square root of 2 is irrational: 1. Assume that √2 is a rational number. Meaning that there exists an integer a and b so that a / b = √2. 2. Then √2 can be written as an irreducible fraction (the fraction is shortened as much as possible) a...

find the inverse of f(x)=3sqrt(x+2) -7 x>=-2 I got this far (x+7)=3sqrt(y+2) I don't know how to get rid of the cube root someone help please :cry:

I tried some formulas on my graph calculator after reading about root mean square calculations of power and physics. Plot these using radians: Y1 = (sin(X)^2)^(1/2) Y2 = (tan(X)^2)^(1/2) Y3 = (tan(X)^3)^(1/3) Axis: 0<x<2(pi) 0<y<2(pi) or zoom to fit! kinda cool huh! Has anyone...

let g be a primitive root of the odd prime p show that -g is a primitive root or not according as p==1 ( mod 4) or p==3(mod4) how would i start in solving this problem thanks :cool:

What do you do when Root(b^2-4ac) is negative? because you can't have a negative under a root right?

\sqrt{x} + \sqrt{x+2} + \sqrt{x}\sqrt{x+2}=16,5-x

roots! HELP For what values of k does the equation x^2+k=kx-8 have two distinct roots, one real root, no real roots? convert into standard form first well x^2+k-kx+8 I don't know if i can simplify this further? and if i can't then what does a=? b=? and c=? I don't understand how to do...

does anyone know how to find the square root of 5+12i ?

Here's a silly roots question that has my congested mind temporarily stumped: Let z = 1 + \sqrt{2}. Find the five distinct fifth roots of z. Thanks in advance for helping me relieve the pressure.