query: why the square root of x equals x to the one half power
positive_passages.docid: 17707
positive_passages.text: Why is ${x^{\frac{1}{2}}}$ the same as $\sqrt x $?
negative_passages.docid: 6582
negative_passages.text: Prove the existence of the square root of $2$.
negative_passages.docid: 33184
negative_passages.text: Something strange about $\sqrt{ 4+ \sqrt{ 4 + \sqrt{ 4-x}}}=x$ and its friends
negative_passages.docid: 144765
negative_passages.text: Solving $\sqrt{x+5} = x - 1$
negative_passages.docid: 77081
negative_passages.text: Proving square root of a square is the same as absolute value
negative_passages.docid: 110661
negative_passages.text: When does $\sqrt{a b} = \sqrt{a} \sqrt{b}$?
negative_passages.docid: 14633
negative_passages.text: What's the thing with $\sqrt{-1} = i$
negative_passages.docid: 117320
negative_passages.text: Why is this true: $\|x\|_1 \le \sqrt n \cdot \|x\|_2$?
negative_passages.docid: 54030
negative_passages.text: Square and square root and negative numbers
negative_passages.docid: 133614
negative_passages.text: Why is $x^{\log_x n}=n$?
negative_passages.docid: 34227
negative_passages.text: Continued fraction of a square root
negative_passages.docid: 144042
negative_passages.text: On the functional square root of $x^2+1$
negative_passages.docid: 101162
negative_passages.text: Square root of $2$ is irrational
negative_passages.docid: 19
negative_passages.text: Why is the square root of a sum not equal to the square root of each its addends?
negative_passages.docid: 85351
negative_passages.text: Standard Deviation. Why do we take the square root of the entire equation?
negative_passages.docid: 127830
negative_passages.text: proof that $\sqrt(2)$ is irrational / why is the fraction irreducible
negative_passages.docid: 157847
negative_passages.text: If $x_n \to 0$, show that $\sqrt{x_n} \to 0$