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Rationalizing denominator — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses rationalizing denominator — a algebra concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.

All of these problems are used with official legal permission of the Mathematical Association of America (MAA).

AMC 10

2001 AMC 10 Problem 20 · 2007 AMC 10A Problem 19 · 2009 AMC 10A Problem 21 · 2011 AMC 10B Problem 16 · 2022 AMC 10A Problem 5

AMC 12

2016 AMC 12A Problem 9 · 2021 AMC 12A Fall Problem 13

AIME

2002 AIME I Problem 2 · 2006 AIME II Problem 9 · 2013 AIME I Problem 5

More algebra concepts

absolute valueagesalgebraic manipulationAM-GM Inequalityarithmetic sequencebinomial theoremcalculusCauchy-Schwarz Inequalitycompleting the squarecomplex numbercustom operationDe Moivre’s Theoremdeterminantdifference of squaresfactoringFibonaccifloor and ceiling functionsfunctionfunctional equationgeometric sequenceinequalitylinear equationlogarithmmatrixmixtureNewton’s Sumspartial fractionspolynomialquadraticradicalrational equationrecursionroots of unitySimon’s Favorite Factoring Trickslopesubstitutionsum and difference of cubessum of first n cubessum of first n odd numberssum of first n squaressummationsymmetry (algebra)system of equationstelescopingVieta’s Formulas