query: What's the proof that $\sqrt {AB} = \sqrt A \times \sqrt B$
positive_passages.docid: 150320
positive_passages.text: Why does $a^{b}·a^{c}=a^{b+c}$?
negative_passages.docid: 80759
negative_passages.text: Proving $A\times (B\cap C)=(A \times B)\cap (A\times C)$.
negative_passages.docid: 67514
negative_passages.text: Formal Proof that area of a rectangle is $ab$
negative_passages.docid: 72747
negative_passages.text: Proving gcd($a,b$)lcm($a,b$) = $|ab|$
negative_passages.docid: 109745
negative_passages.text: If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.
negative_passages.docid: 26570
negative_passages.text: Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
negative_passages.docid: 11506
negative_passages.text: Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer
negative_passages.docid: 61666
negative_passages.text: Proving $ [(\vec{a}+\vec{b})\times(\vec{b}+\vec{c})]\cdot(\vec{c}+\vec{a})=2\vec{c}\cdot(\vec{b}\times\vec{a})$
negative_passages.docid: 31436
negative_passages.text: Show that for all $a\in\mathbb{N}$, there exists $b\in\mathbb{N}$ and square-free integer $c$ such that $\sqrt{a}=b\sqrt{c}$.
negative_passages.docid: 152817
negative_passages.text: Proving $\sup B=\inf A$
negative_passages.docid: 63267
negative_passages.text: Under what conditions on the sets $A$ and $B$ will it be true that $A\times B= B\times A$
negative_passages.docid: 73277
negative_passages.text: Prove $[\sqrt{x}+\sqrt{x+1}]=[\sqrt{4x+2}], x \in \Bbb N$
negative_passages.docid: 10107
negative_passages.text: Prove $A\cup (A\cap B) = A$
negative_passages.docid: 76049
negative_passages.text: Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
negative_passages.docid: 78736
negative_passages.text: Check my proof that $(ab)^{-1} = b^{-1} a^{-1}$
negative_passages.docid: 22215
negative_passages.text: How to prove Binet theorem, namely $\det ( AB ) = \det (A ) \det ( B )$?
negative_passages.docid: 85977
negative_passages.text: Show that if $\sqrt{a}+\sqrt{b}\neq 0$, then $\mathbb{Q}(\sqrt{a}+\sqrt{b}) = \mathbb{Q}(\sqrt{a},\sqrt{b}), \forall a,b\in\mathbb{Q}$