For the field $F=\{a+b\sqrt{3}\}$, find $d$ so that $b\cdot d=1$, where $b,d\in F$
98577
Show that the set $\mathbb{Q}(\sqrt{p})=\{a+b\sqrt{p}; a,b,p\in\mathbb{Q},\sqrt{p}\notin \mathbb{Q}\}$ is a field
28218
Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
8589
$\sqrt[b_1]{a_1}+\sqrt[b_2]{a_2}+\cdots+\sqrt[b_k]{a_k}$ not an integer
27021
Show that $Q[\sqrt3]$ is a field
23712
$F$ is a finite field of size $s$. Prove that if $s=2^m$ for some $m>0$, then all elements of F have a square root.
138501
Is $\mathbf{Q}(\sqrt{2},\sqrt{3}) = \mathbf{Q}(\sqrt{6})$?
119156
$(a,b)=d \overset{?}{\implies} (a^3,b^3)=d^3$
117970
Find the minimal polynomial for $\sqrt[3]{2} + \sqrt[3]{4}$ over $\mathbb{Q}$
112368
Is there a rule for $\sqrt{a+b}$?
87111
Prove $\sqrt{2}$ is between $\dfrac{a}{b}$ and $\dfrac{a+2b}{a+b}$
46565
Show that $\mathbb{Q}(\sqrt{2})$ is a field.
120954
Prove that: $\sqrt[3]{a_1^3+ a_2^3 +\cdots+a_n^3} \le \sqrt{a_1^2 + a_2^2 +\cdots+a_n^2}$
98256
Subfields of $\mathbb{Q}(\sqrt{2},\sqrt{3})$
51518
Is $\sqrt[3]{p+q\sqrt{3}}+\sqrt[3]{p-q\sqrt{3}}=n$, $(p,q,n)\in\mathbb{N} ^3$ solvable?
157496
Determine the Galois group of $\mathbb{Q}(\sqrt{a+b\sqrt{d}})$
66656
I have to find a splitting field of $x^{6}-3$ over $\mathbb{F}_{7}$
144512
Find the greatest value of $a^2\cdot b^3$ where $a+b=10$