query: Is there a general template for Proving the Irrationality of some Radical by Contradiction
positive_passages.docid: 1383
positive_passages.text: How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
negative_passages.docid: 48975
negative_passages.text: Transcendental numbers and irrationality measure
negative_passages.docid: 30478
negative_passages.text: How to prove that a number is irrational
negative_passages.docid: 126633
negative_passages.text: Is a contradiction enough to prove a set equality to $\varnothing$?
negative_passages.docid: 58284
negative_passages.text: How to prove that $\sqrt[3] 2 + \sqrt[3] 4$ is irrational?
negative_passages.docid: 28347
negative_passages.text: Prove that $\sqrt 2 + \sqrt 3$ is irrational
negative_passages.docid: 32848
negative_passages.text: Prove that the product of a non-zero rational and irrational number is irrational.
negative_passages.docid: 132115
negative_passages.text: Verify my proof of the irrationality of $\sqrt{6}$.
negative_passages.docid: 24706
negative_passages.text: Is there a rational number between any two irrationals?
negative_passages.docid: 53945
negative_passages.text: The square root of a prime number is irrational
negative_passages.docid: 101028
negative_passages.text: Irrational numbers and Borel Sets
negative_passages.docid: 144244
negative_passages.text: Bound on difference between irrational square root and rational number
negative_passages.docid: 31744
negative_passages.text: Proving that there is an irrational number between any two unequal rational numbers.
negative_passages.docid: 89716
negative_passages.text: Is there a proof of the irrationality of $\sqrt{2}$ that involves modular arithmetic?
negative_passages.docid: 4946
negative_passages.text: Non-existence of irrational numbers?
negative_passages.docid: 10008
negative_passages.text: Proof that the nth root of a rational s/t is irrational unless s and t are perfect nth powers
negative_passages.docid: 41318
negative_passages.text: Can every proof by contradiction also be shown without contradiction?