# Tagged Questions

For questions involving radical numbers or expressions (i.e. expressions which involve $\sqrt[n]{\text{something}}$).

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### Find the limits : $\lim_{x\to\infty} x\left(\sqrt{x^2+2x}-2\sqrt{x^2+x}+x\right)$ [on hold]

$$\lim_{x\to\infty} x\left(\sqrt{x^2+2x}-2\sqrt{x^2+x}+x\right) =\ ?$$
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### How to show this formula to get a square root of a number in “just few seconds” is true?

I don't remember in which topic I found it but I know it was there. And I still have not find a proof of this nice approximation. Let $x$ be a non perfect square number. If $y$ is the closer ...
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### Is this polynomial solvable by radicals?3

Suppose you have a field $\mathbb{F}$. Show that the polynomial $x^n-n\cdot1_{\mathbb{F}}\in \mathbb{F}[x]$, where $n\geq 2$ is solvable by radicals.
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### What is the fastest method to find which of $\frac {3\sqrt {3}-4}{7-2\sqrt {3}}$ and $\frac {3\sqrt {3}-8}{1-2\sqrt {3}}$ is bigger manually?

What is the fastest method to find which number is bigger manually? $\frac {3\sqrt {3}-4}{7-2\sqrt {3}}$ or $\frac {3\sqrt {3}-8}{1-2\sqrt {3}}$
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### Why we square while doing the proof of √2 is irrational? [closed]

When we prove that $\sqrt 2$ is irrational by the method of contradiction, we assume $\sqrt 2$ is a rational number: $\sqrt 2 = a/b$ Squaring both sides, $2 = a^2/b^2$. Here is my question: is ...
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### How to pull out coefficient from radical in an integral

I am in an online Calculus 2 class, and before my professor gets back to me, I was wondering if you guys could help. I was reading through an example: How was 1/27 pulled out from the coefficient ...
Ramanujan found that $\sqrt[3]{\cos\left(\frac {2\pi}{7}\right)}+\sqrt[3]{\cos\left(\frac {4\pi}{7}\right)}+\sqrt[3]{\cos\left(\frac {8\pi}{7}\right)}=\sqrt[3]{\frac {1}{2}\left(5-3\sqrt[3]{7}\right)}$...