Find $f$ and $g$ by trial and error and a rigorous proof for showing that $\mathbb{Q}[\sqrt{2} + \sqrt{3}] = \mathbb{Q}[\sqrt{2},\sqrt{3}]$
32760
Is $\mathbf{Q}(\sqrt{2}, \sqrt{3}) = \mathbf{Q}(\sqrt{2}+\sqrt{3})$?
55742
Showing that $f_{2n+1}=f_{n+1}^2+f_n^2$.
21457
Prove $\sqrt{2\sqrt{3\sqrt{\cdots\sqrt{n}}}}<3$ by induction.
98496
Let $a,b \in \mathbb{Q^{+}}$ then $\sqrt{a} + \sqrt{b} \in \mathbb{Q} $ iff $\sqrt{a} \in \mathbb{Q}$ and $\sqrt{b} \in \mathbb{Q}$
58284
How to prove that $\sqrt[3] 2 + \sqrt[3] 4$ is irrational?
155165
Prove that $\mathbb F_8=\mathbb F_2[X]/(X^3+X+1)$
142470
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})= \mathbb{Q}(\sqrt{p}\cdot \sqrt[3]{q})$ ??
70128
Prove that $(fg)^{(n)} = \sum_{k=0}^n \binom{n}{k}f^{(k)}(x)g^{(n-k)}(x)$
21972
How to show that $\sqrt{2}+\sqrt{3}$ is algebraic?
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
129521
Is $\sqrt[3]{5}$ in $\mathbb Q(\sqrt[3]{2})$?
63478
Is $\mathbb{Q}(\sqrt{2}) \cong \mathbb{Q}(\sqrt{3})$?
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
95459
$\mathbb{Q}(\sqrt{2+\sqrt{2}})$ is Galois over $\mathbb{Q}$?
41226
Find $f:f(xf(x)+f(y))=f(x)^2+y$
11564
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})=\mathbb{Q}(\sqrt{p}\sqrt[3]{q})$ for distinct prime $p,q$
16163
Show $\mathbb{Q}(\sqrt{2},\sqrt{3})$ is a simple extension field of $\mathbb{Q}$.