Compute the splitting field and the Galois group of $x^4 - 5$ over $\mathbb{Q} (\sqrt{5})$.
50785
Galois group of $x^4-5$
1443
How to find the Galois group of a polynomial?
158588
Determine the Galois group of the polynomial $(x^3-2)(x^3-3)(x^2-2)$ over $\mathbb{Q}(\sqrt {-3})$
75828
Compute Galois group of $\mathbb F_q/\mathbb F_p$
42213
Computing $\text{Gal}(\mathbb{Q}^{ab}/\mathbb{Q})$
134896
Enlightening proof that the algebraic numbers form a field
100162
Minimal polynomial over an extension field divides the minimal polynomial over the base field
103148
Show Galois group of $f(t) = t^5 - 3$ over $\mathbb Q$ is solvable
103238
Conjugates of ${\sqrt 5 + \sqrt 6 }$ over $\mathbb{Q}$ and irreducibility of $x^4 -22x^2+1$ (for minimal polynomial)
148217
A polynomial with integer coefficients that attains the value $5$ at four distinct points
73713
Prove that $\mathbb{Q}(\sqrt{(2+\sqrt{2})(3+\sqrt{3})})$ is Galois over $\mathbb{Q}$ is Galois and determine the Galois group
98256
Subfields of $\mathbb{Q}(\sqrt{2},\sqrt{3})$
50172
Show that $\mathbb{Q}(\sqrt{2})$ is the smallest subfield of $\mathbb{C}$ that contains $\sqrt{2}$
4048
Find the Galois group of $x^3-5$ over $\mathbb{Q}$.
114295
Find all the middle fields of the splitting field of $x^4-2$ over $\mathbb{Q}$
39642
Efficient way to find $[\mathbb{Q}(\sqrt{5}, \sqrt{3}, \sqrt{2}): \mathbb{Q}(\sqrt{3}, \sqrt{2})]$
9422
Computing the Galois group of polynomials $x^n-a \in \mathbb{Q}[x]$