query: Why is $\sqrt{x^2}= |x|$ rather than $\pm x$?
positive_passages.docid: 77081
positive_passages.text: Proving square root of a square is the same as absolute value
negative_passages.docid: 27788
negative_passages.text: Why is the expected value $E(X^2) \neq E(X)^2$?
negative_passages.docid: 96554
negative_passages.text: Why is $x^0 = 1$ except when $x = 0$?
negative_passages.docid: 117320
negative_passages.text: Why is this true: $\|x\|_1 \le \sqrt n \cdot \|x\|_2$?
negative_passages.docid: 70660
negative_passages.text: Why is $\sqrt{8}/2$ equal to $\sqrt{2}$?
negative_passages.docid: 85351
negative_passages.text: Standard Deviation. Why do we take the square root of the entire equation?
negative_passages.docid: 125069
negative_passages.text: Help with $\int \frac 1{\sqrt{a^2 - x^2}} \mathrm dx$
negative_passages.docid: 16420
negative_passages.text: When does $\sqrt{wz}=\sqrt{w}\sqrt{z}$?
negative_passages.docid: 59818
negative_passages.text: Why $(-2)^{2.5}$ isn't equal to $((-2)^{25})^{1/10}$?
negative_passages.docid: 14633
negative_passages.text: What's the thing with $\sqrt{-1} = i$
negative_passages.docid: 88640
negative_passages.text: Is $\sqrt x$ continuous at $0$? Because it is not defined to the left of $0$
negative_passages.docid: 24688
negative_passages.text: Why are $i$ and $-i$ "more indistinguishable" than $\sqrt{2}$ and $-\sqrt{2}$?
negative_passages.docid: 39457
negative_passages.text: Why is \[ ... \] preferable to $$ ... $$?
negative_passages.docid: 31327
negative_passages.text: Why is $\sqrt{x}$ a function?
negative_passages.docid: 50041
negative_passages.text: Significance of $\sqrt[n]{a^n} $?!
negative_passages.docid: 151439
negative_passages.text: $\sqrt{1-x^2}$ is not a rational function
negative_passages.docid: 82630
negative_passages.text: How is it, that $\sqrt{x^2}$ is not $ x$, but $|x|$?