query: Is $\sqrt[3]{x^3}$ monomial?
positive_passages.docid: 152436
positive_passages.text: Are $(x^3)^{1/3} $ and $\sqrt{x^2}$ monomials?
negative_passages.docid: 158588
negative_passages.text: Determine the Galois group of the polynomial $(x^3-2)(x^3-3)(x^2-2)$ over $\mathbb{Q}(\sqrt {-3})$
negative_passages.docid: 73553
negative_passages.text: How is $a_n=(1+1/n)^n$ monotonically increasing and bounded by $3$?
negative_passages.docid: 115834
negative_passages.text: Cubic polynomial with three (distinct) irrational roots
negative_passages.docid: 117789
negative_passages.text: Computing Galois Group of $\mathbb{Q}(\sqrt{2},\sqrt{3}):\mathbb{Q}$
negative_passages.docid: 153444
negative_passages.text: $\mathbb{Q}(\sqrt[3]{2})$ is not in any cyclotomic extension of $\mathbb{Q}$
negative_passages.docid: 92517
negative_passages.text: Easy way to show that $\mathbb{Z}[\sqrt[3]{2}]$ is the ring of integers of $\mathbb{Q}[\sqrt[3]{2}]$
negative_passages.docid: 105395
negative_passages.text: Minimal polynomial of $1 + 2^{1/3} + 4^{1/3}$
negative_passages.docid: 21972
negative_passages.text: How to show that $\sqrt{2}+\sqrt{3}$ is algebraic?
negative_passages.docid: 104498
negative_passages.text: Show that $x^3y^3(x^3+y^3) \leq 2$
negative_passages.docid: 158364
negative_passages.text: Are there uncountably many $A\in M_3 (\mathbb {R})$ such that $A^8=I $?
negative_passages.docid: 58133
negative_passages.text: ${a^2}{\mid}({b^3} + 1)\;$and$\;{b^2}{\mid}({a^3} + 1)$
negative_passages.docid: 37529
negative_passages.text: If $\sqrt[3]{a} + \sqrt[3]{b}$ is rational then prove $\sqrt[3]{a}$ and $\sqrt[3]{b}$ are rational
negative_passages.docid: 112150
negative_passages.text: Prove that the ideal $(x^2 + x+2)$ is maximal in $F_3[x]$
negative_passages.docid: 109952
negative_passages.text: Find the minimal polynomial of $\sqrt2 + \sqrt3 $ over $\mathbb Q$
negative_passages.docid: 55197
negative_passages.text: Roots of $ x^3-3x+1$
negative_passages.docid: 103763
negative_passages.text: Minimal polynomial of $\sqrt{2}+\sqrt{3}$ over $\mathbb Q$