Question

What is the name of this proof of, "$\sqrt{2}$ is irrational"?

score 354 · Answer 1 · 2026-03-25 11:14:49

354

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What is the name of this proof of, "$\sqrt{2}$ is irrational"?

Published on 25 Mar 2026 - 11:14

score 9.8k · Answer 2 · 2026-03-25 11:16:00

9.8k

Views

Understanding the proof of "$\sqrt{2}$ is irrational" by contradiction.

Published on 25 Mar 2026 - 11:16

score 79 · Answer 3 · 2026-03-25 17:45:37

79

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Solvability by radicals of Polynomials defined by a recurrence relation

Published on 25 Mar 2026 - 17:45

score 75 · Answer 4 · 2014-11-16 13:57:47

75

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Calculate the following integral: $\int \sqrt[3]{1+x\ln{x}} \cdot (1+\ln{x}) dx$

Published on 16 Nov 2014 - 13:57

score 1k · Answer 5 · 2026-03-29 00:00:09

1k

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How to evaluate $\lim_{n\to\infty}\sqrt[n]{\frac{1\cdot3\cdot5\cdot\ldots\cdot(2n-1)}{2\cdot4\cdot6\cdot\ldots\cdot2n}}$

Published on 29 Mar 2026 - 0:00

score 534 · Answer 6 · 2026-03-25 17:16:57

534

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Evaluating a decimal exponent

Published on 25 Mar 2026 - 17:16

score 205 · Answer 7 · 2026-03-28 03:03:09

205

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Evaluation of $\lim_{x\rightarrow \infty}\sqrt{x^2+x+1} -\lfloor \sqrt{x^2+x+1 }\rfloor\;,$

Published on 28 Mar 2026 - 3:03

score 252 · Answer 8 · 2014-11-24 20:10:00

252

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Irrational number inequality : $1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}>\sqrt{3}$

Published on 24 Nov 2014 - 20:10

score 1.1k · Answer 9 · 2014-11-27 12:01:25

1.1k

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Evaluate $\int \frac{\sqrt{\sin\sqrt x}\cos \sqrt x}{1+x^2} dx$?

Published on 27 Nov 2014 - 12:01

score 745 · Answer 10 · 2014-11-29 01:08:02

745

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How to find the value of $\ \lim_{x\to 3^+}\frac{\sqrt{x^2-9}}{x-3}$?

Published on 29 Nov 2014 - 1:08

score 72 · Answer 11 · 2026-03-25 12:53:44

72

Views

Can $x^{2q}$ be irrational for rational $x$ and $q$?

Published on 25 Mar 2026 - 12:53

score 78 · Answer 12 · 2026-03-29 03:22:24

78

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How do I prove that $\lim _{n\to \infty} (\sqrt{n^2 + 1} - n) = 0$?

Published on 29 Mar 2026 - 3:22

score 256 · Answer 13 · 2026-03-29 06:28:39

256

Views

Evaluate $ \lim_{n\to \infty}\sqrt[n]{n!}$

Published on 29 Mar 2026 - 6:28

score 193 · Answer 14 · 2014-12-04 15:33:37

193

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How to transform a fraction with square root in denominator?

Published on 04 Dec 2014 - 15:33

score 525 · Answer 15 · 2026-03-25 21:22:47

525

Views

Proving $\left(\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x+\cdots}}}}\right)\left(\sqrt{x-\sqrt{x-\sqrt{x-\sqrt{x+\cdots}}}}\right)=x$

Published on 25 Mar 2026 - 21:22

List Question

What is the name of this proof of, "$\sqrt{2}$ is irrational"?

Understanding the proof of "$\sqrt{2}$ is irrational" by contradiction.

Solvability by radicals of Polynomials defined by a recurrence relation

Calculate the following integral: $\int \sqrt[3]{1+x\ln{x}} \cdot (1+\ln{x}) dx$

How to evaluate $\lim_{n\to\infty}\sqrt[n]{\frac{1\cdot3\cdot5\cdot\ldots\cdot(2n-1)}{2\cdot4\cdot6\cdot\ldots\cdot2n}}$

Evaluating a decimal exponent

Evaluation of $\lim_{x\rightarrow \infty}\sqrt{x^2+x+1} -\lfloor \sqrt{x^2+x+1 }\rfloor\;,$

Irrational number inequality : $1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}>\sqrt{3}$

Evaluate $\int \frac{\sqrt{\sin\sqrt x}\cos \sqrt x}{1+x^2} dx$?

How to find the value of $\ \lim_{x\to 3^+}\frac{\sqrt{x^2-9}}{x-3}$?

Can $x^{2q}$ be irrational for rational $x$ and $q$?

How do I prove that $\lim _{n\to \infty} (\sqrt{n^2 + 1} - n) = 0$?

Evaluate $ \lim_{n\to \infty}\sqrt[n]{n!}$

How to transform a fraction with square root in denominator?

Proving $\left(\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x+\cdots}}}}\right)\left(\sqrt{x-\sqrt{x-\sqrt{x-\sqrt{x+\cdots}}}}\right)=x$

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