List questions from rationality-testing

Published on 06 Jan 2014 - 15:29

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Prove that $\sqrt[n]{\frac{b^{n}}{a^{n}}+1}$ is irrational for every $b,a,n\in\mathbb{ N}$ and $n>2$.

Published on 14 Jan 2014 - 11:59

226

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Find number of integral solutions of $\sqrt{n}+\sqrt{n+7259}$

Published on 22 Jan 2014 - 17:32

4.9k

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Prove that 2.101001000100001... is an irrational number.

Published on 06 Feb 2014 - 17:54

69

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Let $n$ be contained in $\mathbb N$. Show that $ n^{1/2}$ is either an integer or it is irrational.

Published on 12 Feb 2014 - 8:44

11.1k

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Is the cube root of a prime number rational?

Published on 13 Feb 2014 - 17:45

1.9k

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Help understanding this proof: $\sqrt2$ is irrational

Published on 10 Mar 2014 - 17:16

670

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Is this proof by contradiction that 9+13√3 is irrational correct?

Published on 02 May 2017 - 8:52

2.8k

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Prove that the square root of pq when p and q are distinct primes is irrational

Published on 05 May 2017 - 4:39

1.7k

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Irrationality or Rationality of p+q given that pq=1

Published on 21 May 2017 - 19:03

309

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For distinct odd primes $p, q$ we have $\sqrt{p^2 - 4q}$ is always irrational?

Published on 22 May 2017 - 8:37

82

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Can a log be a root?

Published on 25 Mar 2026 - 20:02

125

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Is $\sqrt{4+\pi} + \sqrt{4-\pi} \in \mathbb{Q}$?

Published on 12 Jun 2017 - 10:32

408

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iEquation in Rudin's 1.1.3 (Principles of Mathematical Analysis)

Published on 14 Jun 2017 - 5:09

90

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Are there any proofs for (ir)rationality of the numbers $\sin(e)$, $\cos(e)$?

Published on 13 Jul 2017 - 7:50

List Question

Prove that $\sqrt[3]{5-\sqrt{2}}$ is not a rational number

Prove that $\sqrt[n]{\frac{b^{n}}{a^{n}}+1}$ is irrational for every $b,a,n\in\mathbb{ N}$ and $n>2$.

Find number of integral solutions of $\sqrt{n}+\sqrt{n+7259}$

Prove that 2.101001000100001... is an irrational number.

Let $n$ be contained in $\mathbb N$. Show that $ n^{1/2}$ is either an integer or it is irrational.

Is the cube root of a prime number rational?

Help understanding this proof: $\sqrt2$ is irrational

Is this proof by contradiction that 9+13√3 is irrational correct?

Prove that the square root of pq when p and q are distinct primes is irrational

Irrationality or Rationality of p+q given that pq=1

For distinct odd primes $p, q$ we have $\sqrt{p^2 - 4q}$ is always irrational?

Can a log be a root?

Is $\sqrt{4+\pi} + \sqrt{4-\pi} \in \mathbb{Q}$?

iEquation in Rudin's 1.1.3 (Principles of Mathematical Analysis)

Are there any proofs for (ir)rationality of the numbers $\sin(e)$, $\cos(e)$?

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