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Why is $\sqrt[3]{18+5\sqrt{13}} + \sqrt[3]{18-5\sqrt{13}} = 3$?
algebra-precalculus
radicals
factoring
substitution
nested-radicals
Puzzled by $\lim\limits_{x \to - \infty} \sqrt{x^2+x}-x$
limits
analysis
radicals
Limit of $\frac{\sqrt{1-\cos x}}x$ using l'Hôpital
calculus
limits
trigonometry
radicals
The value of the integral $\int_0^2\left(\sqrt{1+x^3}+\sqrt[3]{x^2+2x}\:\right)dx$
calculus
integration
definite-integrals
closed-form
radicals
How to evaluate $\lim_{n\to\infty}\sqrt[n]{\frac{1\cdot3\cdot5\cdot\ldots\cdot(2n-1)}{2\cdot4\cdot6\cdot\ldots\cdot2n}}$
calculus
limits
factorial
radicals
Conjugation method in solving limits
calculus
limits
radicals
Prove that $\sqrt{3}+ \sqrt{5}+ \sqrt{7}$ is irrational [duplicate]
radicals
rationality-testing
Sum of two irrational radicals is irrational?
abstract-algebra
number-theory
elementary-number-theory
radicals
irrational-numbers
When to neglect the negative value of a square root?
roots
radicals
Conjugate of real number
radicals
real-numbers
rational-numbers
Convergence of $\sum_{n=1}^\infty{\left(\sqrt[n]{n}-1\right)}$
calculus
sequences-and-series
convergence-divergence
radicals
Simplifying $\sqrt{4+2\sqrt{3}}+\sqrt{4-2\sqrt{3}}$
algebra-precalculus
radicals
nested-radicals
Find real roots of the equation
algebra-precalculus
functions
roots
radicals
How to show that $\sqrt{3 - \sqrt{2}} \notin \mathbb{Q}(\sqrt{3 + \sqrt{2}})$ [duplicate]
abstract-algebra
galois-theory
extension-field
radicals
nested-radicals
How to prove that $\frac{a}{\sqrt{a+b}}+\frac{b}{\sqrt{b+c}}+\frac{c}{\sqrt{c+a}}\leq\frac{3\sqrt{3}}{4}$?
trigonometry
inequality
radicals
cauchy-schwarz-inequality
muirhead-inequality
Find formula for $\frac{1}{\sqrt 1}+ \frac{1}{\sqrt 2}+\cdots+\frac{1}{\sqrt n}$
sequences-and-series
summation
radicals
Evaluating Limit Question $\lim\limits_{n\to \infty}\ \frac{1+\sqrt[2]{2}+\sqrt[3]{3}+\cdots+\sqrt[n]{n}}{n}=1$?
real-analysis
calculus
limits
radicals
how can I solve the following equation (without complex numbers)?
algebra-precalculus
radicals
Evaluation of $\lim\limits_{n\to\infty} (\sqrt{n^2 + n} - \sqrt[3]{n^3 + n^2}) $
calculus
limits
proof-verification
radicals
$p,q,r$ primes, $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is irrational.
number-theory
proof-verification
alternative-proof
radicals
rationality-testing
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