query: Rationalizing the denominator with radicals
positive_passages.docid: 75503
positive_passages.text: Rationalizing a Denominator with Cube Roots
negative_passages.docid: 23752
negative_passages.text: Proving Irrationality
negative_passages.docid: 35110
negative_passages.text: Predicting the number of decimal digits needed to express a rational number
negative_passages.docid: 115834
negative_passages.text: Cubic polynomial with three (distinct) irrational roots
negative_passages.docid: 130162
negative_passages.text: A complete residue system from an arithmetic progression
negative_passages.docid: 114011
negative_passages.text: Algebra - Solving for three unknowns.
negative_passages.docid: 129946
negative_passages.text: Synthetic division of polynomials by factor of the form $(ax+b)$
negative_passages.docid: 99366
negative_passages.text: Minimum of an expression involving radicals: $\sqrt{\frac{2a}{a+b}} + \sqrt{\frac{2b}{b+c}} + \sqrt{\frac{2c}{c+a}}$
negative_passages.docid: 127304
negative_passages.text: Understanding the algebra of polynomials on a linear space
negative_passages.docid: 126230
negative_passages.text: Simplifying radicals for limit leads to extra minus symbol
negative_passages.docid: 114442
negative_passages.text: Completion of rational numbers via Cauchy sequences
negative_passages.docid: 50445
negative_passages.text: Explaining the product of two ideals
negative_passages.docid: 107349
negative_passages.text: Working with elementary type proofs of divisor functions
negative_passages.docid: 127664
negative_passages.text: Inverse elements in the absence of identities/associativity.
negative_passages.docid: 23112
negative_passages.text: Solving an equation with rational expressions (step by step)
negative_passages.docid: 86603
negative_passages.text: Infinite square-rooting
negative_passages.docid: 89056
negative_passages.text: Intuitive understanding of ideal $I = (x+1,x^2+1)$ and the quotient $\Bbb Z[x]/I$