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]]
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* [[2006 AIME I Problems]]

Revision as of 12:13, 30 June 2006

Problem

The number

$\sqrt{104\sqrt{6}+468\sqrt{10}+144\sqrt{15}+2006}$

can be written as $a\sqrt{2}+b\sqrt{3}+c\sqrt{5},$ where $a, b,$ and $c$ are positive integers. Find $a\cdot b\cdot c.$



Solution

See also