Show $\sqrt{1+\sqrt{2}}$ is algebraic over $\mathbb{Q}$ with degree $4$
38489
Degree of the extension $\mathbb{Q}(\sqrt{a+\sqrt{b}})$ over $\mathbb{Q}$
38549
$\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$
95602
Computing the Galois group of $x^4+ax^2+b \in \mathbb{Q}[x] $
24168
A characterisation of quadratic extensions contained in cyclic extensions of degree 4
112427
Irreducibility of $p(x)=x^4-4x^2+8x+2$ over $\mathbb{Q}(\sqrt{-2})$- Dummit Foote Abstract algebra $9.4.10$
145140
Subfield of $\mathbb{Q}(\sqrt[n]{a})$
24551
How to prove that the sum and product of two algebraic numbers is algebraic?
43300
The degree of $\sqrt{2} + \sqrt[3]{5}$ over $\mathbb Q$
66946
show that $(i+k)! > i!k!$ algebraically
98496
Let $a,b \in \mathbb{Q^{+}}$ then $\sqrt{a} + \sqrt{b} \in \mathbb{Q} $ iff $\sqrt{a} \in \mathbb{Q}$ and $\sqrt{b} \in \mathbb{Q}$
127764
Showing that $\mathbb{Q}[\sqrt{2}, \sqrt{3}]$ contains multiplicative inverses
98256
Subfields of $\mathbb{Q}(\sqrt{2},\sqrt{3})$
111291
Galois group of $\mathbb Q(\sqrt{4+\sqrt 7})/\mathbb Q$
50172
Show that $\mathbb{Q}(\sqrt{2})$ is the smallest subfield of $\mathbb{C}$ that contains $\sqrt{2}$
155750
Why does $\mathbb{C}$ have transcendence degree $\mathfrak{c}$ over $\mathbb{Q}$?
103238
Conjugates of ${\sqrt 5 + \sqrt 6 }$ over $\mathbb{Q}$ and irreducibility of $x^4 -22x^2+1$ (for minimal polynomial)
63280
Show that the set $\mathbb{Q}[\sqrt{2}] = \{a + b \sqrt{2} \mid a, b \in \mathbb{Q}\}$ is a field with the usual multiplication and addition.