Determine the Galois group of $X^4 - 2X^2 +2$ over $\Bbb Q$ and prove $\sqrt 2 \in \Bbb Q(\alpha)$ where $\alpha$ is a root of $X^4 - 2X^2 +2$
95602
Computing the Galois group of $x^4+ax^2+b \in \mathbb{Q}[x] $
103148
Show Galois group of $f(t) = t^5 - 3$ over $\mathbb Q$ is solvable
56420
Is $\mathbb{Q}(\sqrt[3]{3}, \sqrt[4]{3})$ a Galois extension of $\mathbb{Q}$
93546
Galois group and the Quaternion group
158588
Determine the Galois group of the polynomial $(x^3-2)(x^3-3)(x^2-2)$ over $\mathbb{Q}(\sqrt {-3})$
22158
Find the quadratic sub field of $\mathbb Q(\zeta_7)$ which can be expressed in the form $\mathbb Q(\sqrt D)$,where $D$ is an integer.
99835
Polynomial in $\mathbb{Q}[x]$ with root $\sqrt[3]{2}+\sqrt[3]{3}$
6984
Inverting $a+b\sqrt{2}$ in the field $\Bbb Q(\sqrt{2})$
130826
Computing class group of $\mathbb Q(\sqrt{6})$
93196
$x^4 -10x^2 +1 $ is irreducible over $\mathbb Q$
50785
Galois group of $x^4-5$
41069
Justifying $\,\Bbb{Z}[i]/\langle 2\rangle\cong \Bbb{Z}[X]/\langle X^2+1,2\rangle\cong \Bbb{F}_2[X]/\langle X^2+1\rangle$
99516
Show $\mathbb{Q}[\sqrt[3]{2}]$ is a field by rationalizing
86957
Galois group of irreducible cubic equation
42677
Proving $(\alpha + \beta)^{p^n} = \alpha^{p^n} + \beta^{p^n}$ in a finite field
119878
"Standard" ways of telling if an irreducible quartic polynomial has Galois group C_4?
77403
Finding the minimal polynomial of $\sqrt 2 + \sqrt[3] 2$ over $\mathbb Q$.