Why $\sqrt[3]{{2 + \sqrt 5 }} + \sqrt[3]{{2 - \sqrt 5 }}$ is a rational number?
27802
How to show this equals 1 without "calculations"
95702
Remarkable/unexpected rational numbers
128298
Irrationality of sum of two logarithms: $\log_2 5 +\log_3 5$
21121
Express $w$ and $1/w$ for $w=\frac {\sqrt2+\sqrt3}{\sqrt5-\sqrt3}$ in the simplest form with a rational denominator
70315
Process to show that $\sqrt 2+\sqrt[3] 3$ is irrational
84017
Is $\sqrt[3]{2}$ contained in $\mathbb{Q}(\zeta_n)$?
149675
Simplifying $\sqrt[4]{161-72 \sqrt{5}}$
138193
Why is $\sqrt {12} = 2 \sqrt 3$?
75349
Minimal polynomial of $\sqrt[3]{2} + \sqrt{3}$
4048
Find the Galois group of $x^3-5$ over $\mathbb{Q}$.
116054
The number $(3+\sqrt{5})^n+(3-\sqrt{5})^n$ is an integer
65645
Express $w$ and $\frac1w$ for $w=\frac {\sqrt2+\sqrt3}{\sqrt5-\sqrt3}$ in the simplest form with a rational denominator
139755
Prove that $\sqrt{2}+\sqrt{3}+\sqrt{5}$ is irrational. Generalise this.
126074
Proof of the irrationality of $\sqrt{3}$ - logic question
7500
$\arctan$ of a square root as a rational multiple of $\pi$
51518
Is $\sqrt[3]{p+q\sqrt{3}}+\sqrt[3]{p-q\sqrt{3}}=n$, $(p,q,n)\in\mathbb{N} ^3$ solvable?
8589
$\sqrt[b_1]{a_1}+\sqrt[b_2]{a_2}+\cdots+\sqrt[b_k]{a_k}$ not an integer