List questions from radical-equations

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Zero set of nested radicals

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Integrate $\frac{x}{(x^4+1)^2 \sqrt{(x^2-x+1)}}$.

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Trick to this square root equations

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Inequality with square root on both sides

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Surds question grade 10

Published on 10 May 2026 - 14:19

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"Extraneous solution" solves original equation

Published on 25 Mar 2026 - 1:13

62

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A radical equation $(2x+1)^{2/3}+(2x-1)^{2/3}-2x^{2/3}=2^{1/3}$

Published on 25 Mar 2026 - 3:07

127

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Are there any simpler ways to determine the solution for $\sqrt{x+\sqrt{x}}=1$ without back substitution checks?

Published on 25 Mar 2026 - 1:17

38

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What is the rate of convergence of the following sequence (equation with a finite number of nested radicals)?

Published on 13 Apr 2026 - 0:18

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What are some obscure radical identities?

Published on 25 Mar 2026 - 7:42

124

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square root of x equals -1

Published on 06 Apr 2026 - 1:42

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solution-verification | Show that if $a$ and $q$ are natural numbers and the number $(a+\sqrt{q})(a+\sqrt{q+1})$ is rational, then $q=0$.

Published on 25 Mar 2026 - 1:18

59

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Prove that there are infinitely many distinct natural numbers $a,b$ for which $\sqrt{a+b}, \sqrt{a-b}$ are simultaneously rational

Published on 25 Mar 2026 - 1:17

45

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Is the de Moivre's formula only intended to be used for unknown values of the input $z$, but not to fixed values of $z$?

Published on 25 Mar 2026 - 1:18

List Question

Determining the extraneous solution to a radical equation

Zero set of nested radicals

Integrate $\frac{x}{(x^4+1)^2 \sqrt{(x^2-x+1)}}$.

Trick to this square root equations

Inequality with square root on both sides

Surds question grade 10

"Extraneous solution" solves original equation

A radical equation $(2x+1)^{2/3}+(2x-1)^{2/3}-2x^{2/3}=2^{1/3}$

Are there any simpler ways to determine the solution for $\sqrt{x+\sqrt{x}}=1$ without back substitution checks?

What is the rate of convergence of the following sequence (equation with a finite number of nested radicals)?

What are some obscure radical identities?

square root of x equals -1

solution-verification | Show that if $a$ and $q$ are natural numbers and the number $(a+\sqrt{q})(a+\sqrt{q+1})$ is rational, then $q=0$.

Prove that there are infinitely many distinct natural numbers $a,b$ for which $\sqrt{a+b}, \sqrt{a-b}$ are simultaneously rational

Is the de Moivre's formula only intended to be used for unknown values of the input $z$, but not to fixed values of $z$?

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