Alternative proof for $[\mathbb{Q}(\sqrt{p},\sqrt{q}):\mathbb{Q}]=4$
27784
Proving that $\left(\mathbb Q[\sqrt p_1,\dots,\sqrt p_n]:\mathbb Q\right)=2^n$ for distinct primes $p_i$.
112427
Irreducibility of $p(x)=x^4-4x^2+8x+2$ over $\mathbb{Q}(\sqrt{-2})$- Dummit Foote Abstract algebra $9.4.10$
111291
Galois group of $\mathbb Q(\sqrt{4+\sqrt 7})/\mathbb Q$
58009
How to show that $\mathbb Q(\sqrt 2)$ is not field isomorphic to $\mathbb Q(\sqrt 3).$
156766
Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$
58284
How to prove that $\sqrt[3] 2 + \sqrt[3] 4$ is irrational?
104300
Help justifying that $\mathbb Q(\sqrt[3]{2})$ is not a splitting field over $\mathbb Q$.
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
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.
35216
Prove $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}$ is a simple extension
158161
$\mathbb{Q}(\sqrt p_{1}+\sqrt p_{2})=\mathbb{Q}(\sqrt p_{1},\sqrt p_{2})$ for $p_{1},p_{2}$ primes.
34491
Is there a way to show that $\sqrt{p_{n}} < n$?
43300
The degree of $\sqrt{2} + \sqrt[3]{5}$ over $\mathbb Q$
69046
Proof of $\mathbb{Q}$ is not cyclic
46730
How to show $\mathbb{Q}(\alpha^{4})=\mathbb{Q}(\alpha)$?
16163
Show $\mathbb{Q}(\sqrt{2},\sqrt{3})$ is a simple extension field of $\mathbb{Q}$.
98256
Subfields of $\mathbb{Q}(\sqrt{2},\sqrt{3})$