The square root of a prime number is irrational
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
44440
Prove $\sqrt{2}+\sqrt[3]{5}$ is irrational
28347
Prove that $\sqrt 2 + \sqrt 3$ is irrational
147777
If $P$ and $Q$ are distinct primes, how to prove that $\sqrt{PQ}$ is irrational?
55077
prove that $2\sqrt5 +\sqrt{11}$ is irrational
103323
Finding a primitive root of a prime number
17930
Please explain this step in proving the square root of 3 is irrational
15110
About irrational logarithms
13592
How can $\pi$ be irrational if it can be calculated using an infinite series of rational numbers?
64885
Irrational and rational sequence proof
6275
How can you prove that the square root of two is irrational?
43985
Why must $a$ and $b$ both be coprime when proving that the square root of two is irrational?
30411
The closure of the irrational numbers on $\mathbb{R}$
141424
$\log_7 n$ is either an integer or an irrational number
34710
Cardinality of Irrational Numbers
32
Is $n^{th}$ root of $2$ an irrational number?
10008
Proof that the nth root of a rational s/t is irrational unless s and t are perfect nth powers