Question

How can we show that $\sqrt{a}+\sqrt{b}+\sqrt{c}$ is a rational number only if $a,b,c$ are perfect squares?

score 562 · Answer 1 · 2023-10-06 16:22:49

562

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How can we show that $\sqrt{a}+\sqrt{b}+\sqrt{c}$ is a rational number only if $a,b,c$ are perfect squares?

Published on 06 Oct 2023 - 16:22

score 123 · Answer 2 · 2026-03-25 06:01:53

123

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square root of x equals -1

Published on 25 Mar 2026 - 6:01

score 31 · Answer 3 · 2026-03-28 11:42:50

31

Views

Proving associativity of binary operation

Published on 28 Mar 2026 - 11:42

score 45 · Answer 4 · 2026-03-27 18:09:30

45

Views

Rationalization of $\frac{1}{\sum_{i=1}^{n}\sqrt{a_i}}$ (symmetric formula with multi-index)

Published on 27 Mar 2026 - 18:09

score 128 · Answer 5 · 2023-10-28 08:12:43

128

Views

Finding $\sqrt 2$ in terms of $\sqrt 2 + \sqrt[3]3$

Published on 28 Oct 2023 - 8:12

score 855 · Answer 6 · 2026-03-28 09:44:19

855

Views

What's wrong with this limit solution?

Published on 28 Mar 2026 - 9:44

score 29 · Answer 7 · 2023-10-31 20:31:17

29

Views

Real-base powers and fractional exponent

Published on 31 Oct 2023 - 20:31

score 123 · Answer 8 · 2023-11-03 09:39:45

Finding $\small{\max\limits_{ab+bc+ca=1}\sqrt{\frac{1}{a+1}+\frac{1}{b+1}}+\sqrt{\frac{1}{a+1}+\frac{1}{c+1}}+\sqrt{\frac{1}{c+1}+\frac{1}{b+1}}.}$

score 121 · Answer 9 · 2023-11-05 09:37:21

121

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Finding $\small{\min\limits_{a+b+c=2(ab+bc+ca)}\sum_{cyc}\sqrt{\dfrac{1}{ab}+\dfrac{1}{bc}+1}.}$

Published on 05 Nov 2023 - 9:37

score 74 · Answer 10 · 2026-02-23 08:05:00

74

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Prove $f(a,b,c)\le f\left(\frac{a+b}{2},\frac{a+b}{2},c\right)$

Published on 23 Feb 2026 - 8:05

score 371 · Answer 11 · 2023-11-06 07:12:54

371

Views

Solving $y+\sqrt{y^2-1}=e^x$ respect to $y$

Published on 06 Nov 2023 - 7:12

score 125 · Answer 12 · 2023-11-10 10:11:13

125

Views

Evaluate limit to infinity of roots of $n$ [ $\lim\limits_{n \to \infty} \sqrt n (\sqrt[n]{n}-1)$ ]

Published on 10 Nov 2023 - 10:11

score 34 · Answer 13 · 2023-11-10 23:19:30

34

Views

Definition of simple radical extension.

Published on 10 Nov 2023 - 23:19

score 253 · Answer 14 · 2023-11-11 09:27:01

253

Views

evaluate the limit when x goes to infinity

Published on 11 Nov 2023 - 9:27

score 76 · Answer 15 · 2023-11-12 12:59:45

76

Views

How to express $y$ from $x^2+y^2>r$?

Published on 12 Nov 2023 - 12:59

List Question

How can we show that $\sqrt{a}+\sqrt{b}+\sqrt{c}$ is a rational number only if $a,b,c$ are perfect squares?

square root of x equals -1

Proving associativity of binary operation

Rationalization of $\frac{1}{\sum_{i=1}^{n}\sqrt{a_i}}$ (symmetric formula with multi-index)

Finding $\sqrt 2$ in terms of $\sqrt 2 + \sqrt[3]3$

What's wrong with this limit solution?

Real-base powers and fractional exponent

Finding $\small{\max\limits_{ab+bc+ca=1}\sqrt{\frac{1}{a+1}+\frac{1}{b+1}}+\sqrt{\frac{1}{a+1}+\frac{1}{c+1}}+\sqrt{\frac{1}{c+1}+\frac{1}{b+1}}.}$

Finding $\small{\min\limits_{a+b+c=2(ab+bc+ca)}\sum_{cyc}\sqrt{\dfrac{1}{ab}+\dfrac{1}{bc}+1}.}$

Prove $f(a,b,c)\le f\left(\frac{a+b}{2},\frac{a+b}{2},c\right)$

Solving $y+\sqrt{y^2-1}=e^x$ respect to $y$

Evaluate limit to infinity of roots of $n$ [ $\lim\limits_{n \to \infty} \sqrt n (\sqrt[n]{n}-1)$ ]

Definition of simple radical extension.

evaluate the limit when x goes to infinity

How to express $y$ from $x^2+y^2>r$?

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