Question

If $a$ and $b$ are rational, then $a + b{\sqrt{2}} \ne {\sqrt{3}} $

score 91 · Answer 1 · 2026-04-05 17:16:42

91

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If $a$ and $b$ are rational, then $a + b{\sqrt{2}} \ne {\sqrt{3}} $

Published on 05 Apr 2026 - 17:16

score 9.4k · Answer 2 · 2026-03-30 04:44:24

9.4k

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How to prove $\sqrt{5+\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5-\cdots}}}}}}} = \frac{2+\sqrt 5 +\sqrt{15-6\sqrt 5}}{2}$

Published on 30 Mar 2026 - 4:44

score 911 · Answer 3 · 2013-10-05 10:36:00

911

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How to solve the limit $\lim_{n \to \infty} \sqrt[8]{n^2+1} - \sqrt[4]{n+1}$?

Published on 05 Oct 2013 - 10:36

score 5.4k · Answer 4 · 2013-10-06 02:19:13

5.4k

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How does $\cos(2\pi/257)$ look like in real radicals?

Published on 06 Oct 2013 - 2:19

score 1k · Answer 5 · 2013-10-06 10:42:16

1k

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Solve $\sqrt{a+bx}+\sqrt{b+cx}+\sqrt{c+ax}=\sqrt{b-ax}+\sqrt{c-bx}+\sqrt{a-cx}$

Published on 06 Oct 2013 - 10:42

score 947 · Answer 6 · 2026-04-02 13:03:59

947

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How to find $\lfloor 1/\sqrt{1}+1/\sqrt{2}+\dots+1/\sqrt{100}\rfloor $ without a calculator?

Published on 02 Apr 2026 - 13:03

score 199 · Answer 7 · 2013-10-06 19:29:48

199

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The sum of three square roots bounded below by $\sqrt{82}$

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score 1.8k · Answer 8 · 2026-04-06 23:35:27

1.8k

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Are there infinitely many natural numbers whose square root is rational?

Published on 06 Apr 2026 - 23:35

score 4.1k · Answer 9 · 2013-10-07 16:25:07

4.1k

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Evaluate the limit of $(\sqrt{5-x}-2)/(\sqrt{2-x}-1)$ as $x\to 1$

Published on 07 Oct 2013 - 16:25

score 1.2k · Answer 10 · 2026-04-09 03:26:14

1.2k

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How is it, that $\sqrt{x^2}$ is not $ x$, but $|x|$?

Published on 09 Apr 2026 - 3:26

score 3k · Answer 11 · 2026-04-09 09:03:42

3k

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Published on 09 Apr 2026 - 9:03

score 363 · Answer 12 · 2026-04-02 13:03:58

363

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Find $\lim_{n\rightarrow \infty}\left(\sqrt{n^2+n+1}-\big\lfloor \sqrt{n^2+n+1} \big\rfloor \right)$

Published on 02 Apr 2026 - 13:03

score 707 · Answer 13 · 2013-10-10 21:44:27

707

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Proof by contradiction that $\sqrt{2} + \sqrt{6} < \sqrt{15}$

Published on 10 Oct 2013 - 21:44

score 110 · Answer 14 · 2026-04-08 17:26:55

110

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Problem finding in simple algebra

Published on 08 Apr 2026 - 17:26

score 2.5k · Answer 15 · 2013-10-12 00:53:46

2.5k

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Radical expression for Cosine formulas

Published on 12 Oct 2013 - 0:53

List Question

If $a$ and $b$ are rational, then $a + b{\sqrt{2}} \ne {\sqrt{3}} $

How to prove $\sqrt{5+\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5-\cdots}}}}}}} = \frac{2+\sqrt 5 +\sqrt{15-6\sqrt 5}}{2}$

How to solve the limit $\lim_{n \to \infty} \sqrt[8]{n^2+1} - \sqrt[4]{n+1}$?

How does $\cos(2\pi/257)$ look like in real radicals?

Solve $\sqrt{a+bx}+\sqrt{b+cx}+\sqrt{c+ax}=\sqrt{b-ax}+\sqrt{c-bx}+\sqrt{a-cx}$

How to find $\lfloor 1/\sqrt{1}+1/\sqrt{2}+\dots+1/\sqrt{100}\rfloor $ without a calculator?

The sum of three square roots bounded below by $\sqrt{82}$

Are there infinitely many natural numbers whose square root is rational?

Evaluate the limit of $(\sqrt{5-x}-2)/(\sqrt{2-x}-1)$ as $x\to 1$

How is it, that $\sqrt{x^2}$ is not $ x$, but $|x|$?

simplify fraction with radical in numerator, first steps?

Find $\lim_{n\rightarrow \infty}\left(\sqrt{n^2+n+1}-\big\lfloor \sqrt{n^2+n+1} \big\rfloor \right)$

Proof by contradiction that $\sqrt{2} + \sqrt{6} < \sqrt{15}$

Problem finding in simple algebra

Radical expression for Cosine formulas

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