query: Find the value of $\frac{\sqrt2 + \sqrt6}{\sqrt{2 + \sqrt3}}$
positive_passages.docid: 22512
positive_passages.text: Find the value of: $\frac{\sqrt{45} + \sqrt{18}} {\sqrt{7+2\sqrt{10}}}$
negative_passages.docid: 82317
negative_passages.text: Find the minimum value of $A=\frac{2-a^3}{a}+\frac{2-b^3}{b}+\frac{2-c^3}{c}$
negative_passages.docid: 99328
negative_passages.text: Value of $\sin (2^\circ)\cdot \sin (4^\circ)\cdot \sin (6^\circ)\cdots \sin (90^\circ) $
negative_passages.docid: 48154
negative_passages.text: Find the minimum value of $f(x,y,z)=\frac{x^2}{(x+y)(x+z)}+\frac{y^2}{(y+z)(y+x)}+\frac{z^2}{(z+x)(z+y)}$.
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}}$
negative_passages.docid: 46401
negative_passages.text: Value of $\frac{\sqrt{10+\sqrt{1}}+\sqrt{10+\sqrt{2}}+\cdots+\sqrt{10+\sqrt{99}} }{\sqrt{10-\sqrt{1}}+\sqrt{10-\sqrt{2}}+\cdots+\sqrt{10-\sqrt{99}}}$
negative_passages.docid: 145578
negative_passages.text: How find the value $\beta$ such $\left|\frac{p}{q}-\sqrt{2}\right|<\frac{\beta}{q^2}$
negative_passages.docid: 99930
negative_passages.text: Find the Maximum value of $\frac{x}{\sqrt{x+y}}+\frac{y}{\sqrt{y+z}}+\frac{z}{\sqrt{z+x}}$
negative_passages.docid: 1190
negative_passages.text: Square Root of Rational Number $\frac{A}{B}$
negative_passages.docid: 26287
negative_passages.text: Find $\frac{a^2}{2a^2+bc}+\frac{b^2}{2b^2+ac}+\frac{c^2}{2c^2+ab}$ if $a+b+c=0$
negative_passages.docid: 23576
negative_passages.text: Calculating $1+\frac13+\frac{1\cdot3}{3\cdot6}+\frac{1\cdot3\cdot5}{3\cdot6\cdot9}+\frac{1\cdot3\cdot5\cdot7}{3\cdot6\cdot9\cdot12}+\dots? $
negative_passages.docid: 29190
negative_passages.text: $\left\lfloor \frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+...+\frac{1}{\sqrt{1024}}\right\rfloor =?$
negative_passages.docid: 4816
negative_passages.text: How to solve $\frac 1{1.2.3}+\frac 1{2.3.4}+\frac 1{3.4.5}+...$
negative_passages.docid: 8919
negative_passages.text: If $\alpha = \frac{2\pi}{7}$ then the find the value of $\tan\alpha .\tan2\alpha +\tan2\alpha \tan4\alpha +\tan4\alpha \tan\alpha.$
negative_passages.docid: 62463
negative_passages.text: A pencil approach to find $\sum \limits_{i=1}^{69} \sqrt{\left( 1+\frac{1}{i^2}+\frac{1}{(i+1)^2}\right)}$
negative_passages.docid: 65645
negative_passages.text: Express $w$ and $\frac1w$ for $w=\frac {\sqrt2+\sqrt3}{\sqrt5-\sqrt3}$ in the simplest form with a rational denominator
negative_passages.docid: 54078
negative_passages.text: The minimum value of $\frac{(x+\frac{1}{x})^6-(x^6+\frac{1}{x^6})-2}{(x+\frac{1}{x})^3+x^3+\frac{1}{x^3}}$