List questions from radicals

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What is the error in this square root denesting?

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How to quickly solve $ 2 + \frac94t = \left( \frac{27+16\sqrt{2}}{8} \right)^{\frac23} $?

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Proof by cases that there is an irrational number $a$ such that $a^{\sqrt{3}}$ is rational?

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Cubic root epsilon delta proof

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Triangles geometric inequalities

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Find $x^5+x^{-5}$ given the value of $x^2+x^{-2}$.

Published on 29 May 2018 - 14:58

69

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Prove that $\frac{1}{\sqrt {a^2 - b^2}} = \frac{1/a}{\sqrt {1 - \frac{b^2}{a^2}}}$

Published on 29 May 2018 - 18:08

444

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Given three non-negative numbers $x,y,z$ so that $x+y+z=3$. Prove that $3\leqq \sum\limits_{cyc}x\sqrt{1+ y^{3}}\leqq 5$ .

Published on 25 Mar 2026 - 4:43

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Why is $z=\sqrt{2i}$ equal to $z=1+i$?

Published on 04 Jun 2018 - 10:32

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Is this a quadratic equation? If not, how do you solve it?

Published on 06 Jun 2018 - 8:07

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Meaning of "Solve over the reals?"

Published on 06 Jun 2018 - 19:51

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Proving the following inequality without using AM-GM inequality.

Published on 24 Mar 2026 - 1:49

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Comparing some numbers $a=2016^\sqrt{2014}, b=2015^\sqrt{2015},c=2014^\sqrt{2016}$

Published on 07 Jun 2018 - 7:06

921

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How could a square root of fraction have a negative root?

Published on 08 Jun 2018 - 0:08

List Question

A tricky algebraic inequality

What is the error in this square root denesting?

How to quickly solve $ 2 + \frac94t = \left( \frac{27+16\sqrt{2}}{8} \right)^{\frac23} $?

Proof by cases that there is an irrational number $a$ such that $a^{\sqrt{3}}$ is rational?

Cubic root epsilon delta proof

Triangles geometric inequalities

Find $x^5+x^{-5}$ given the value of $x^2+x^{-2}$.

Prove that $\frac{1}{\sqrt {a^2 - b^2}} = \frac{1/a}{\sqrt {1 - \frac{b^2}{a^2}}}$

Given three non-negative numbers $x,y,z$ so that $x+y+z=3$. Prove that $3\leqq \sum\limits_{cyc}x\sqrt{1+ y^{3}}\leqq 5$ .

Why is $z=\sqrt{2i}$ equal to $z=1+i$?

Is this a quadratic equation? If not, how do you solve it?

Meaning of "Solve over the reals?"

Proving the following inequality without using AM-GM inequality.

Comparing some numbers $a=2016^\sqrt{2014}, b=2015^\sqrt{2015},c=2014^\sqrt{2016}$

How could a square root of fraction have a negative root?

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