Question

Prove the following inequality $6 \cdot 3^\frac18-5 > 3^{\frac14}$

score 141 · Answer 1 · 2026-03-25 06:06:33

141

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Prove the following inequality $6 \cdot 3^\frac18-5 > 3^{\frac14}$

Published on 25 Mar 2026 - 6:06

score 122 · Answer 2 · 2017-01-09 08:19:46

122

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$f:\mathbb{R}^{+}_0\to\mathbb{R}^{+}_0, x\mapsto\sqrt[n]{x}$ is continuous proof

Published on 09 Jan 2017 - 8:19

score 254 · Answer 3 · 2026-03-29 03:22:21

254

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How is $\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}} = \sqrt{2}-1$?

Published on 29 Mar 2026 - 3:22

score 2.4k · Answer 4 · 2026-03-29 03:21:35

2.4k

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How to factorize this $\sqrt{8 - 2\sqrt{7}}$?

Published on 29 Mar 2026 - 3:21

score 830 · Answer 5 · 2026-03-26 01:09:35

830

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Proof that $2^{1/3} - 1/( 2 ^ {1/3} $) is irrational

Published on 26 Mar 2026 - 1:09

score 594 · Answer 6 · 2026-03-25 07:41:59

594

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Ramanujan's Class Invariant $G_{625}$

Published on 25 Mar 2026 - 7:41

score 482 · Answer 7 · 2017-01-10 20:38:50

482

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Subtracting two square roots

Published on 10 Jan 2017 - 20:38

score 193 · Answer 8 · 2017-01-10 23:07:59

193

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Why does $x^{\frac{1}{a}} = \sqrt[a]{x}$?

Published on 10 Jan 2017 - 23:07

score 1.6k · Answer 9 · 2017-01-11 05:29:17

1.6k

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How to integrate $\int {\frac{1}{x\sqrt{x+1}}\mathrm{d}x}$ using $u$ and $s$ substitution or $u^2$ substitution.

Published on 11 Jan 2017 - 5:29

score 748 · Answer 10 · 2017-01-11 18:37:19

748

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Why do we need rationalisation?

Published on 11 Jan 2017 - 18:37

score 82.6k · Answer 11 · 2026-03-31 20:10:45

82.6k

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Approximating square roots using binomial expansion.

Published on 31 Mar 2026 - 20:10

score 322 · Answer 12 · 2026-03-29 16:00:49

322

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How to prove that $(x+ {\sqrt{1+x^2}} ) ( y+ {\sqrt {1+y^2}}) = 1$ if $(x+ {\sqrt{1+y^2}} ) ( y+ {\sqrt {1+x^2}}) = 1$

Published on 29 Mar 2026 - 16:00

score 553 · Answer 13 · 2017-01-12 13:17:03

553

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Solving $3\sqrt{7x-5}-4=8$

Published on 12 Jan 2017 - 13:17

score 578 · Answer 14 · 2026-03-28 03:33:22

578

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Is there any sense to this notion of $\sqrt{(-1)}\cdot\sqrt{(-1)} = 1$?

Published on 28 Mar 2026 - 3:33

score 2k · Answer 15 · 2026-04-01 02:50:20

2k

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Limit at infinity of cubic roots and square roots without using conjugate $\lim_{x \to \infty} \frac{\sqrt[3]{x+2}}{\sqrt{x+3}}$

Published on 01 Apr 2026 - 2:50

List Question

Prove the following inequality $6 \cdot 3^\frac18-5 > 3^{\frac14}$

$f:\mathbb{R}^{+}_0\to\mathbb{R}^{+}_0, x\mapsto\sqrt[n]{x}$ is continuous proof

How is $\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}} = \sqrt{2}-1$?

How to factorize this $\sqrt{8 - 2\sqrt{7}}$?

Proof that $2^{1/3} - 1/( 2 ^ {1/3} $) is irrational

Ramanujan's Class Invariant $G_{625}$

Subtracting two square roots

Why does $x^{\frac{1}{a}} = \sqrt[a]{x}$?

How to integrate $\int {\frac{1}{x\sqrt{x+1}}\mathrm{d}x}$ using $u$ and $s$ substitution or $u^2$ substitution.

Why do we need rationalisation?

Approximating square roots using binomial expansion.

How to prove that $(x+ {\sqrt{1+x^2}} ) ( y+ {\sqrt {1+y^2}}) = 1$ if $(x+ {\sqrt{1+y^2}} ) ( y+ {\sqrt {1+x^2}}) = 1$

Solving $3\sqrt{7x-5}-4=8$

Is there any sense to this notion of $\sqrt{(-1)}\cdot\sqrt{(-1)} = 1$?

Limit at infinity of cubic roots and square roots without using conjugate $\lim_{x \to \infty} \frac{\sqrt[3]{x+2}}{\sqrt{x+3}}$

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