In the following proof that square root of 2 is non-terminating, where does the expression for q come from?
67161
No maximum(minimum) of rationals whose square is lesser(greater) than $2$.
87111
Prove $\sqrt{2}$ is between $\dfrac{a}{b}$ and $\dfrac{a+2b}{a+b}$
106716
The sum of square roots of non-perfect squares is never integer
44391
How can I prove $n - 2\sqrt{n} = \Theta(n)$
134927
How can a square root be defined since it has two answers?
143733
Is this proof that $\sqrt 2$ is irrational correct?
134885
proving that $\mathbb{Q}(\sqrt{5}, \sqrt{6}) = \mathbb{Q}(\sqrt{5}+ \sqrt{6}) $
35216
Prove $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}$ is a simple extension
84017
Is $\sqrt[3]{2}$ contained in $\mathbb{Q}(\zeta_n)$?
10111
Prove or disprove that Q[√2] is a field
39170
Existence of square root
60261
Is $\sqrt{x^2}=|x|$ or $=x$? Isn't $(x^2)^\frac12=x?$
150624
Why does the square root of a square involve the plus-minus sign?
33184
Something strange about $\sqrt{ 4+ \sqrt{ 4 + \sqrt{ 4-x}}}=x$ and its friends
43985
Why must $a$ and $b$ both be coprime when proving that the square root of two is irrational?
44307
Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
114506
Expansion of $(1+\sqrt{2})^n$