Prove that a rational number minus an irrational number must be irrational.
3790
Rational + irrational = always irrational?
28347
Prove that $\sqrt 2 + \sqrt 3$ is irrational
132478
Prove that continuous functions mapping irrationals to rationals must be constant
126074
Proof of the irrationality of $\sqrt{3}$ - logic question
41767
Sequence of rational numbers converging to an arbitrary irrational number $\beta$.
69264
Is there an irrational number $a$ such that $a^a$ is rational?
91101
Proving $\sqrt2$ is irrational
37915
$\sqrt{2}$ is irrational proof using well-Ordering Property
44440
Prove $\sqrt{2}+\sqrt[3]{5}$ is irrational
147777
If $P$ and $Q$ are distinct primes, how to prove that $\sqrt{PQ}$ is irrational?
48035
Prove that square root of 2 is irrational using the principle of Mathematical Induction
158066
Prove $2^{1/3}$ is irrational.
55077
prove that $2\sqrt5 +\sqrt{11}$ is irrational
19076
If a.b.c,d are rationals and x is irrational number, then prove that $\frac{ax+b}{cx+d}$ is usually a irrational number. When do exceptions occur?
114793
Prove that $\sqrt{10} - \sqrt6 - \sqrt5 + \sqrt3$ is irrational
13592
How can $\pi$ be irrational if it can be calculated using an infinite series of rational numbers?
48975
Transcendental numbers and irrationality measure