Perfect cube: Difference between revisions
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A '''perfect cube''' is an [[integer]] that is equal to some other integer raised to the third power. We refer to raising a [[number]] to the third power as ''cubing'' the number. | A '''perfect cube''' is an [[integer]] that is equal to some other integer raised to the third power. We refer to raising a [[number]] to the third power as ''cubing'' the number. | ||
For example, 125 is a perfect cube because <math>5^3 = 125</math>. However, 121 is not a cube because there is no integer <math>n</math> such that <math>n^3 = 121</math>. | For example, 125 is a perfect cube because <math>5^3 = 125</math>. However, 121 is not a perfect cube because there is no integer <math>n</math> such that <math>n^3 = 121</math>. | ||
== Example Problems == | == Example Problems == | ||
=== Introductory Problems === | === Introductory Problems === | ||
* [[2005_AMC_10A_Problems/Problem_15 | 2005 AMC 10A Problem 15]] | * [[2005_AMC_10A_Problems/Problem_15 | 2005 AMC 10A Problem 15]] | ||
* [[2018_AMC_8_Problems/Problem_25 | 2018 AMC 8 Problem 25]] | |||
=== Intermediate Problems === | |||
*[[1988_AIME_Problems/Problem_9 | 1988 AIME Problem 9]] | |||
== See also == | == See also == | ||
Latest revision as of 13:12, 24 August 2023
A perfect cube is an integer that is equal to some other integer raised to the third power. We refer to raising a number to the third power as cubing the number.
For example, 125 is a perfect cube because 
. However, 121 is not a perfect cube because there is no integer 
such that 
.
