Tagged Questions
1
vote
2answers
64 views
How do I evaluate the following expression?
How to evaluate the following expression:
$\displaystyle \frac{1}{\sqrt{2}+1}+ \frac{1}{\sqrt{3}+\sqrt{2}}+\frac{1}{\sqrt{4}+\sqrt{3}} +\cdots +\frac{1}{\sqrt{9}+\sqrt{8}}$
7
votes
4answers
274 views
Algorithms for “solving” $\sqrt{2}$
The very first words out of my mouth need to be this... "Solving" is the wrong term since I am speaking about irrational numbers. I just don't know which word is the correct word... So that can be ...
4
votes
0answers
34 views
Digits of two irrational numbers, given their power with fixed number of digits
I have $a, b \in \mathbb{R} \setminus \mathbb{Q}$, I want to know the result of $a^b$, but I don't know exact $a, b$ because I write them in numeric form.
My question is how many digits of $a, b$ have ...
3
votes
5answers
125 views
Proof of Easy Theorem?
I was reading the proof of this theorem and have a little trouble understanding one part of it:
Theorem: If $k > 2$ and $n$ are natural numbers, then $n^{\frac{1}{k}}$ is irrational unless $n$ is ...
5
votes
1answer
906 views
Sum of irrational numbers
Well, in this question it is said that $\sqrt[100]{\sqrt3 + \sqrt2} + \sqrt[100]{\sqrt3 - \sqrt2}$, and the owner asks for "alternative proofs" which do not use rational root theorem. I wrote an ...
0
votes
1answer
94 views
non-perfect square of number [duplicate]
Possible Duplicate:
$a^{1/2}$ is either an integer or an irrational number
I would like to know the better proof for the following one.
question: non perfect square of any integer is an ...
1
vote
2answers
114 views
-$\frac{2\sqrt{2}-6}{7}$ = $\frac{6-2\sqrt{2}}{7}$ correct?
When asked to rationalize the denominator for $\frac{2}{\sqrt{2}+3}$, I came up with $\frac{6-2\sqrt{2}}{7}$ but my algebra book gives -$\frac{2\sqrt{2}-6}{7}$ as the answer. I think we're both ...
3
votes
4answers
395 views
why does $\sqrt2 = \frac{2}{\sqrt2}$?
I noticed just now that $\sqrt2 = \frac{2}{\sqrt2}$
I'm suprised because isn't this like saying $x = \frac{2}{x}$?
