New posts in radicals

Solving a radical equation for real $x$

algebra-precalculus functions roots radicals

Can the general septic be solved by infinitely nested radicals?

roots radicals nested-radicals

How would I simplify this function $\rho(x)=x+\sqrt{x-\sqrt{x-\sqrt{x+\sqrt{\dots}}}}$

calculus functions radicals nested-radicals

Isn't square root a bit like Log()?

logarithms arithmetic exponentiation radicals

How prove that $xyz+\sqrt{x^2y^2+y^2z^2+x^2z^2}\ge \frac{4}{3}\sqrt{xyz(x+y+z)}$

real-analysis inequality radicals substitution uvw

Understanding the proof of "$\sqrt{2}$ is irrational" by contradiction.

elementary-number-theory logic proof-verification radicals rationality-testing

$\sqrt{3}$ represented as continued fraction

radicals continued-fractions

Strange approximation to $\sqrt{\pi}$

sequences-and-series approximation radicals irrational-numbers pi

Cancel down the fraction $\dfrac{(x-y)(\sqrt[3]{x}+\sqrt[3]{y})}{\sqrt[3]{x^2}-\sqrt[3]{y^2}}$ [closed]

algebra-precalculus radicals

Given a field $\mathbb F$, is there a smallest field $\mathbb G\supseteq\mathbb F$ where every element in $\mathbb G$ has an $n$th root for all $n$?

abstract-algebra field-theory extension-field radicals axiom-of-choice

Solve $ 1 + \frac{\sqrt{x+3}}{1+\sqrt{1-x}} = x + \frac{\sqrt{2x+2}}{1+\sqrt{2-2x}} $

algebra-precalculus radicals

Show that $\sqrt[3]{3\sqrt{21} + 8} - \sqrt[3]{3\sqrt{21} - 8} = 1$

algebra-precalculus arithmetic radicals

Explanation for $\lim_{x\to\infty}\sqrt{x^2-4x}-x=-2$ and not $0$

calculus limits arithmetic intuition radicals

On Ramanujan's approximation, $n!\sim \sqrt{\pi}\big(\frac ne\big)^n\sqrt [6]{(2n)^3+(2n)^2+n+\frac 1{30}}$

limits proof-writing asymptotics approximation radicals

Are the square roots of all non-perfect squares irrational? [duplicate]

radicals irrational-numbers square-numbers

Find $\lim_{n\rightarrow \infty}\left(\sqrt{n^2+n+1}-\big\lfloor \sqrt{n^2+n+1} \big\rfloor \right)$

calculus sequences-and-series limits radicals ceiling-and-floor-functions

How to solve this limit: $\lim_{x\to\infty}\sqrt{x+\sqrt{x}}-\sqrt{x-1}$ [duplicate]

calculus limits radicals

Proving that $\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\dots+\frac{1}{\sqrt{100}}<20$

inequality summation induction problem-solving radicals

$\sqrt{6}-\sqrt{2}-\sqrt{3}$ is irrational

algebra-precalculus solution-verification radicals rationality-testing

How to prove $\log n \leq \sqrt n$ over natural numbers?

inequality logarithms radicals