Question

Can $\sqrt{a}^\sqrt{b}$ be rational if $\sqrt{a}$ and $\sqrt{b}$ are irrational?

score 674 · Answer 1 · 2026-03-25 16:02:13

674

Views

Can $\sqrt{a}^\sqrt{b}$ be rational if $\sqrt{a}$ and $\sqrt{b}$ are irrational?

Published on 25 Mar 2026 - 16:02

score 1k · Answer 2 · 2026-03-25 09:29:16

1k

Views

Is $x^{1-\frac{1}{n}}+ (1-x)^{1-\frac{1}{n}}$ always irrational if $x$ is rational?

Published on 25 Mar 2026 - 9:29

score 149 · Answer 3 · 2014-10-03 06:45:32

149

Views

Why doesn't this method of solution work?

Published on 03 Oct 2014 - 6:45

score 82 · Answer 4 · 2026-03-25 09:23:20

82

Views

Decide if radical expression equals a given rational number

Published on 25 Mar 2026 - 9:23

score 187 · Answer 5 · 2014-10-07 03:09:41

187

Views

Find the limit of $\sqrt{x^2+x-1} +x$ as $x\to-\infty$

Published on 07 Oct 2014 - 3:09

score 307 · Answer 6 · 2014-10-07 11:47:46

307

Views

How to deduce the following trig relation?

Published on 07 Oct 2014 - 11:47

score 129 · Answer 7 · 2014-10-07 18:57:39

129

Views

How can I find x and z if: $\sqrt{(x-20)^{2} + (5-30)^{2} + (z-40)^{2}} = 100$ and $x \sqrt\frac{1}{6} + 5\sqrt\frac{1}{3} + z \sqrt\frac12= 0$?

Published on 07 Oct 2014 - 18:57

score 804 · Answer 8 · 2026-03-28 20:04:25

804

Views

Simplifying a square root fraction

Published on 28 Mar 2026 - 20:04

score 54 · Answer 9 · 2014-10-08 15:55:16

54

Views

How to show that$\ \sqrt[3]{ \sqrt{y^2-x}+y}+ \sqrt[3]{-\sqrt{y^2-x}+y} = k \implies y = \frac{k\left(k^2-3 \sqrt[3]{x}\right)}{2}$?

Published on 08 Oct 2014 - 15:55

score 448 · Answer 10 · 2026-03-25 09:25:40

448

Views

Show that $(\sqrt{2}-1)^n$ is irrational

Published on 25 Mar 2026 - 9:25

score 145 · Answer 11 · 2026-03-25 09:32:04

145

Views

Proof of $\sqrt{n^2-4}, n\ge 3$ being irrational

Published on 25 Mar 2026 - 9:32

score 149 · Answer 12 · 2014-10-09 18:56:20

149

Views

Prove that $2\sqrt{n}\sqrt{n+1} < 2n + 1$ for all positive integers.

Published on 09 Oct 2014 - 18:56

score 370 · Answer 13 · 2026-03-25 12:33:04

370

Views

How to solve this equation in radicals?

Published on 25 Mar 2026 - 12:33

score 123 · Answer 14 · 2014-10-11 08:51:46

123

Views

Is $\sum i^{1/i}$ bounded?

Published on 11 Oct 2014 - 8:51

score 79 · Answer 15 · 2014-10-11 17:29:00

79

Views

Any general hints on how to prove that two functions$\ f(n)$ and$\ g(m_1,m_2,...,m_{28})$ never have a common natural divisor?

Published on 11 Oct 2014 - 17:29

List Question

Can $\sqrt{a}^\sqrt{b}$ be rational if $\sqrt{a}$ and $\sqrt{b}$ are irrational?

Is $x^{1-\frac{1}{n}}+ (1-x)^{1-\frac{1}{n}}$ always irrational if $x$ is rational?

Why doesn't this method of solution work?

Decide if radical expression equals a given rational number

Find the limit of $\sqrt{x^2+x-1} +x$ as $x\to-\infty$

How to deduce the following trig relation?

How can I find x and z if: $\sqrt{(x-20)^{2} + (5-30)^{2} + (z-40)^{2}} = 100$ and $x \sqrt\frac{1}{6} + 5\sqrt\frac{1}{3} + z \sqrt\frac12= 0$?

Simplifying a square root fraction

How to show that$\ \sqrt[3]{ \sqrt{y^2-x}+y}+ \sqrt[3]{-\sqrt{y^2-x}+y} = k \implies y = \frac{k\left(k^2-3 \sqrt[3]{x}\right)}{2}$?

Show that $(\sqrt{2}-1)^n$ is irrational

Proof of $\sqrt{n^2-4}, n\ge 3$ being irrational

Prove that $2\sqrt{n}\sqrt{n+1} < 2n + 1$ for all positive integers.

How to solve this equation in radicals?

Is $\sum i^{1/i}$ bounded?

Any general hints on how to prove that two functions$\ f(n)$ and$\ g(m_1,m_2,...,m_{28})$ never have a common natural divisor?

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