Square root Definition and 378 Threads

is the square root of a prime number always going to be irrational? just a random question.

Consider the square root operation. Suppose an integer numbers i > 0 as input variable. Design an algorithm which calculates the greatest natural number less than or equal to the square root of the input variable i. can smby pls explain to me what does this ques mean??if possible explain...

Couldn’t decide if I should put this in the calculus or general math forums but... I’m studying for a final that’s coming up this Wednesday and I’ve been looking at some past quizzes with the steps to finding the solutions that my instructor has posted online. Given the problem: 1. Compute...

Hey all, this is my first post here, I have just discovered the site, and it looks great :smile: I need some help on units, regarding square roots. When you find the reciprocal of a quantity, like say, mass, the new unit is kg-1. I'm not sure about when you find the square root of a...

My class, teacher included, cannot seem to figure out the integral of the square root of tan x. Maybe someone here can help? thanks, jeremy

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.

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

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 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?

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

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...

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 -...

\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}=?

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.

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?

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...

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

Hello all I am having trouble proving the limit of the following: lim sqrt(( n+1) - sqrt(n)) * sqrt(n+ 1/2 ) = 1/2 n --> 00 I tried using the fact the the limit of the first factor as n approaches infinity is 0. Then I tried expressing the first factor as 1 /...

Is the square root of 0 undefined? I was recently told that the square root of 0 is undefined because the limit of a square root didn't exist at 0. The reason is that from the negative direction you have i and from the positive direction you don't. At first, i agreed with this. It made enough...

Hi, is \sqrt{a^2-a^2\sin^2{x}} = a\cos{x}? If not, what should it be? :confused: Appreciate the help! :smile:

The square root of pi is 1.777245... I know. But my math teacher says its impossible to determine a square root of an irrational number. Can anyone shed any light on this? is it or is it not possible to determine the square root (or any root) of an irrational number?