query: Is $\sqrt{x^2} = (\sqrt x)^2$?
positive_passages.docid: 157868
positive_passages.text: Is it wrong to say $ \sqrt{x} \times \sqrt{x} =\pm x,\forall x \in \mathbb{R}$?
negative_passages.docid: 158148
negative_passages.text: Find all polynomials $P(x)$ such that $P(x^2)=P(x)^2$
negative_passages.docid: 58901
negative_passages.text: Why is every such function constant: $f(x)=f(x^2)$ for $x \in [0,1]$?
negative_passages.docid: 151439
negative_passages.text: $\sqrt{1-x^2}$ is not a rational function
negative_passages.docid: 119429
negative_passages.text: Why do $x^{x^{x^{\dots}}}=2$ and $x^{x^{x^{\dots}}}=4$ have the same positive root $\sqrt 2$?
negative_passages.docid: 136933
negative_passages.text: Which $n$ can be expressed as $x^2 − y^2$?
negative_passages.docid: 146180
negative_passages.text: Prove that $x\sqrt{1-x^2} \leq \sin x \leq x$
negative_passages.docid: 144042
negative_passages.text: On the functional square root of $x^2+1$
negative_passages.docid: 39170
negative_passages.text: Existence of square root
negative_passages.docid: 152436
negative_passages.text: Are $(x^3)^{1/3} $ and $\sqrt{x^2}$ monomials?
negative_passages.docid: 82630
negative_passages.text: How is it, that $\sqrt{x^2}$ is not $ x$, but $|x|$?
negative_passages.docid: 20532
negative_passages.text: Are these solutions of $2 = x^{x^{x^{\:\cdot^{\:\cdot^{\:\cdot}}}}}$ correct?
negative_passages.docid: 138501
negative_passages.text: Is $\mathbf{Q}(\sqrt{2},\sqrt{3}) = \mathbf{Q}(\sqrt{6})$?
negative_passages.docid: 24307
negative_passages.text: Is $x^x=y$ solvable for $x$?
negative_passages.docid: 14633
negative_passages.text: What's the thing with $\sqrt{-1} = i$
negative_passages.docid: 96204
negative_passages.text: Irrational number $\sqrt2$ proof
negative_passages.docid: 32760
negative_passages.text: Is $\mathbf{Q}(\sqrt{2}, \sqrt{3}) = \mathbf{Q}(\sqrt{2}+\sqrt{3})$?