Why is the proof that $\sqrt2$ is irrational must $p$ and $q$ be coprime?
127830
proof that $\sqrt(2)$ is irrational / why is the fraction irreducible
11564
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})=\mathbb{Q}(\sqrt{p}\sqrt[3]{q})$ for distinct prime $p,q$
44440
Prove $\sqrt{2}+\sqrt[3]{5}$ is irrational
48035
Prove that square root of 2 is irrational using the principle of Mathematical Induction
139755
Prove that $\sqrt{2}+\sqrt{3}+\sqrt{5}$ is irrational. Generalise this.
158161
$\mathbb{Q}(\sqrt p_{1}+\sqrt p_{2})=\mathbb{Q}(\sqrt p_{1},\sqrt p_{2})$ for $p_{1},p_{2}$ primes.
30622
Proving $\sqrt 3$ is irrational.
56877
Show that $\sqrt{4 + 2\sqrt{3}} - \sqrt{3}$ is rational.
96204
Irrational number $\sqrt2$ proof
122226
Incorrect logic in popular proof of the irrationality of $\sqrt2$?
10882
irrationality of $\sqrt{2}^{\sqrt{2}}$.
75204
Irrationality $\sqrt{2}$ with ideal
129521
Is $\sqrt[3]{5}$ in $\mathbb Q(\sqrt[3]{2})$?
158066
Prove $2^{1/3}$ is irrational.
132115
Verify my proof of the irrationality of $\sqrt{6}$.
35837
How to prove that any (integer)$^{1/n}$ that isn't an integer, is irrational?
10111
Prove or disprove that Q[√2] is a field