List questions from radicals

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Inequality for contests

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Maximise $(x+1)\sqrt{1-x^2}$ without calculus

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Injectivity proof

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Series of Nested Radicals

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If $0<x<y$, then prove that $\sqrt{x} <\sqrt{y}$ and $x <\sqrt{xy} <y$

Published on 19 Oct 2018 - 3:53

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Prove or disprove inequality with 3 variables

Published on 19 Oct 2018 - 8:55

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limit $ \lim_{x \to 0} \frac{\sqrt{x}}{\sqrt{x+1} + \sqrt{x}} $

Published on 20 Oct 2018 - 4:36

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How to simplify nested radicals?

Published on 25 Mar 2026 - 5:59

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Solve $\sqrt{\frac{4-x}x}+\sqrt{\frac{x-4}{x+1}}=2-\sqrt{x^2-12}$

Published on 25 Feb 2026 - 2:29

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To prove any real Galois extension of $\mathbb{Q}$ of odd degree must not be radical

Published on 21 Oct 2018 - 19:34

170

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Prove $\sum_{1}^{\infty} \frac{1}{\sqrt{n}( n + \sqrt{n})} \lt 2 $

Published on 25 Mar 2026 - 3:02

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Does taking an n-th root of a negative number lead to contradictions?

Published on 22 Oct 2018 - 18:02

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How to prove $\sqrt {a-\sqrt {a+\sqrt {a-\sqrt {a+\sqrt {a-\sqrt {a+\ldots}}}}}}=\frac {\sqrt {4a-3}-1}2$

Published on 25 Mar 2026 - 6:07

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Finding dependencies such that $0 > \frac{2b^2r^2}{z}-\left(2r ^2-2br\sqrt{1-\frac{b^2}{z^2}}\right)z$

Published on 23 Oct 2018 - 13:33

List Question

Does $\sqrt{i^4} = i^2$?

Inequality for contests

Maximise $(x+1)\sqrt{1-x^2}$ without calculus

Injectivity proof

Series of Nested Radicals

If $0<x<y$, then prove that $\sqrt{x} <\sqrt{y}$ and $x <\sqrt{xy} <y$

Prove or disprove inequality with 3 variables

limit $ \lim_{x \to 0} \frac{\sqrt{x}}{\sqrt{x+1} + \sqrt{x}} $

How to simplify nested radicals?

Solve $\sqrt{\frac{4-x}x}+\sqrt{\frac{x-4}{x+1}}=2-\sqrt{x^2-12}$

To prove any real Galois extension of $\mathbb{Q}$ of odd degree must not be radical

Prove $\sum_{1}^{\infty} \frac{1}{\sqrt{n}( n + \sqrt{n})} \lt 2 $

Does taking an n-th root of a negative number lead to contradictions?

How to prove $\sqrt {a-\sqrt {a+\sqrt {a-\sqrt {a+\sqrt {a-\sqrt {a+\ldots}}}}}}=\frac {\sqrt {4a-3}-1}2$

Finding dependencies such that $0 > \frac{2b^2r^2}{z}-\left(2r ^2-2br\sqrt{1-\frac{b^2}{z^2}}\right)z$

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