Showing $5^{1/3}$ is not in the field $\mathbb{Q}(2^{1/3})$
129521
Is $\sqrt[3]{5}$ in $\mathbb Q(\sqrt[3]{2})$?
50172
Show that $\mathbb{Q}(\sqrt{2})$ is the smallest subfield of $\mathbb{C}$ that contains $\sqrt{2}$
133312
Are these polynomials irreducible in $\mathbb{Q}[x]$?
64878
Is this polynomial irreducible in $\mathbb{Q}$?
140430
Let $E = \mathbb{Q}\big(\left\{\sqrt[n]{2} \mid n \in \mathbb{N} \setminus \left\{0\right\} \right\} \big)$. Prove $[E: \mathbb{Q}]$ is not finite
46565
Show that $\mathbb{Q}(\sqrt{2})$ is a field.
30404
Is $\mathbb{Z}/3\otimes \mathbb{Z}[1/2]=\mathbb{Z}/3$?
156766
Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$
39346
Let $R= \mathbb{Q}[x^2 ,x^3 ]$, the set of all polynomials over $\mathbb{Q}$ with no $x$ term. Show that the $\gcd$ of $x^5$ and $x^6$ does not exist
39642
Efficient way to find $[\mathbb{Q}(\sqrt{5}, \sqrt{3}, \sqrt{2}): \mathbb{Q}(\sqrt{3}, \sqrt{2})]$
153444
$\mathbb{Q}(\sqrt[3]{2})$ is not in any cyclotomic extension of $\mathbb{Q}$
50668
Show that $\mathbb{Q}(\sqrt2, \sqrt[3]2)$ is a primitive field extension of $\mathbb{Q}$.
134885
proving that $\mathbb{Q}(\sqrt{5}, \sqrt{6}) = \mathbb{Q}(\sqrt{5}+ \sqrt{6}) $
145140
Subfield of $\mathbb{Q}(\sqrt[n]{a})$
108550
Elements of $\mathbb Q(2^{1/3})$
19525
Showing field extension $\mathbb{Q}(\sqrt{2}, \sqrt{3}, \sqrt{5})/\mathbb{Q}$ degree 8
112191
How can I show $q^k$ does not divide ${{n}\choose{q}}$ when $q$ is a prime factor of $n$ and $k$ is the largest integer such that $q^k$ divides $n$?