How do I prove that the sum of a rational and irrational number is irrational?
3790
Rational + irrational = always irrational?
125267
Prove that $2^{1/2}$ is irrational
31744
Proving that there is an irrational number between any two unequal rational numbers.
23752
Proving Irrationality
129433
$\sqrt{m_1}+\sqrt{m_2}+ \cdots + \sqrt{m_n}$ is Irrational
83145
Sum of rational numbers
147777
If $P$ and $Q$ are distinct primes, how to prove that $\sqrt{PQ}$ is irrational?
44600
How can I prove: if $p $ is prime and $n>1$, then $ p^{\frac1n} $ is irrational?
41767
Sequence of rational numbers converging to an arbitrary irrational number $\beta$.
104548
Geometric proof for irrationality of $\pi$
44440
Prove $\sqrt{2}+\sqrt[3]{5}$ is irrational
118374
Is there a proof that $\pi$ is an irrational number?
143733
Is this proof that $\sqrt 2$ is irrational correct?
127830
proof that $\sqrt(2)$ is irrational / why is the fraction irreducible
67031
use contradiction to prove that the square root of $p$ is irrational
34710
Cardinality of Irrational Numbers
2926
The contradiction method used to prove that the square root of a prime is irrational