Difference between revisions of "2006 AIME I Problems/Problem 5"
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== Problem == | == Problem == | ||
The number <center><math> \sqrt{104\sqrt{6}+468\sqrt{10}+144\sqrt{15}+2006}</math></center> can be written as <math> a\sqrt{2}+b\sqrt{3}+c\sqrt{5}, </math> where <math> a, b, </math> and <math> c </math> are positive integers. Find <math> a\cdot b\cdot c. </math> | The number <center><math> \sqrt{104\sqrt{6}+468\sqrt{10}+144\sqrt{15}+2006}</math></center> can be written as <math> a\sqrt{2}+b\sqrt{3}+c\sqrt{5}, </math> where <math> a, b, </math> and <math> c </math> are positive integers. Find <math> a\cdot b\cdot c. </math> | ||
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== Solution == | == Solution == | ||
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== See also == | == See also == | ||
| − | * [[2006 AIME I]] | + | * [[2006 AIME I Problems]] |
Revision as of 11:13, 30 June 2006
Problem
The number
can be written as 
where 
and 
are positive integers. Find 
