query: Denest $\sqrt{5^{\frac{1}{3}}-4^{\frac{1}{3}}}$
positive_passages.docid: 143409
positive_passages.text: Simplify $\sqrt {\sqrt[3]{5}-\sqrt[3]{4}}$.
negative_passages.docid: 67853
negative_passages.text: Prove existence of $\lim_{(x,y) \rightarrow (0,2)} \frac{x (y-2)^3}{3x - 5(y-2)^4}$
negative_passages.docid: 97813
negative_passages.text: Squeeze/Sandwich Theorem Involving $n^{th}$ root: $\lim _{ n\rightarrow \infty }{\left(3^n+1\right)}^{\frac 1n}$
negative_passages.docid: 144039
negative_passages.text: Computing $ \int_0^{\infty} \frac{ \sqrt [3] {x+1}-\sqrt [3] {x}}{\sqrt{x}} \mathrm dx$
negative_passages.docid: 7404
negative_passages.text: Induction and convergence of an inequality: $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots(2n)}\leq \frac{1}{\sqrt{2n+1}}$
negative_passages.docid: 100568
negative_passages.text: Showing $\gamma < \sqrt{1/3}$ without a computer
negative_passages.docid: 101371
negative_passages.text: show that $f^{(3)}(c) \ge 3$ for $c\in(-1,1)$
negative_passages.docid: 127396
negative_passages.text: When is $f=\left(\frac{\sqrt{p+4}}{1-p}-1\right)x^5-3x+\ln5$ decreasing $\forall\; x$?
negative_passages.docid: 59352
negative_passages.text: Computing: $\int_0^1 \sqrt[3]{x\log{\frac{1}x}} \, \mathrm dx$
negative_passages.docid: 21121
negative_passages.text: Express $w$ and $1/w$ for $w=\frac {\sqrt2+\sqrt3}{\sqrt5-\sqrt3}$ in the simplest form with a rational denominator
negative_passages.docid: 124699
negative_passages.text: How to calculate $\lim_{n \to \infty}\sqrt[n]{\frac{2^n+3^n}{3^n+4^n}}$
negative_passages.docid: 147506
negative_passages.text: Calculate $\lim\limits_{x\to4} \frac {\sqrt {1+2x}-3} {\sqrt x -2}$
negative_passages.docid: 74570
negative_passages.text: Finding distribution of $\frac{X_1+X_2 X_3}{\sqrt{1+X_3^2}}$
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: 13902
negative_passages.text: Show that $\frac{1}{x_1^2}+\frac{1}{4\cdot x_2^2}+\ldots+\frac{1}{n^2\cdot x_n^2}\leq\frac{3n-2}{2n-1}$.
negative_passages.docid: 24202
negative_passages.text: The value of the trilogarithm at $\frac{1}{2}$
negative_passages.docid: 116649
negative_passages.text: Value of: $ \frac {1} {\sqrt {4} + \sqrt {5}} + \frac {1} {\sqrt {5} + \sqrt {6}} + ... + \frac {1} {\sqrt {80} + \sqrt {81}}$