query: Limit of $a_1=\sqrt{3}$, $a_2=\sqrt{3\sqrt{3}}$, $a_3=\sqrt{3\sqrt{3\sqrt{3}}}$...
positive_passages.docid: 27756
positive_passages.text: Find a formula for a sequence $\{\sqrt{3},\sqrt{3\sqrt{3}},\sqrt{3\sqrt{3\sqrt{3}}},...\}$
negative_passages.docid: 142470
negative_passages.text: $\mathbb{Q}(\sqrt{p},\sqrt[3]{q})= \mathbb{Q}(\sqrt{p}\cdot \sqrt[3]{q})$ ??
negative_passages.docid: 40463
negative_passages.text: Evaluating $\lim _{x\to 1}\left(\frac{\sqrt[3]{x}-1}{2\sqrt{x}-2}\right)$
negative_passages.docid: 136297
negative_passages.text: Evaluate $\lim_{x \to 1} \frac{\sqrt[3]{x} -1}{\sqrt{x} -1}$
negative_passages.docid: 69309
negative_passages.text: How do I simplify and evaluate the limit of $(\sqrt x - 1)/(\sqrt[3] x - 1)$ as $x\to 1$?
negative_passages.docid: 10451
negative_passages.text: Finding the limit of roots products $(\sqrt{2}-\sqrt[3]{2})(\sqrt{2}-\sqrt[4]{2})(\sqrt{2}-\sqrt[5]{2})\cdot \cdot \cdot (\sqrt{2}-\sqrt[n]{2})$
negative_passages.docid: 125860
negative_passages.text: Showing that $\lim\limits_{n\to\infty}x_n$ exists, where $x_{n} = \sqrt{1 + \sqrt{2 + \sqrt{3 + ...+\sqrt{n}}}}$
negative_passages.docid: 64329
negative_passages.text: Limit of the recursive sequence $a_{n+1} = \frac{1}{2}(a_n + \frac{p}{a_n})$
negative_passages.docid: 75705
negative_passages.text: Finding derivative of $\sqrt[3]{x}$ using only limits
negative_passages.docid: 133244
negative_passages.text: Finding $\lim_{n \to \infty} n(\sqrt[n]{2} - 1)$
negative_passages.docid: 110588
negative_passages.text: Showing $\lim_{n\rightarrow\infty}\sqrt[3]{n^3+n^2}-\sqrt[3]{n^3+1}\rightarrow\frac{1}{3}$
negative_passages.docid: 68838
negative_passages.text: Why $\sqrt[3]{3}\not\in \mathbb{Q}(\sqrt[3]{2})$?
negative_passages.docid: 119145
negative_passages.text: $\lim\limits_{n\rightarrow\infty} \sqrt{n}(\sqrt{n+1}-\sqrt{n})$
negative_passages.docid: 5151
negative_passages.text: $ \lim x^2 = a^2$ as $x$ goes to $a$
negative_passages.docid: 48716
negative_passages.text: Evaluating the limit of $\lim_{x \to 9} \frac {x-9} {\sqrt{x} - 3}$
negative_passages.docid: 37529
negative_passages.text: If $\sqrt[3]{a} + \sqrt[3]{b}$ is rational then prove $\sqrt[3]{a}$ and $\sqrt[3]{b}$ are rational
negative_passages.docid: 12301
negative_passages.text: Show that $\lim_{n \rightarrow \infty} \sqrt[n]{a} =1$