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2006 AIME I Problems/Problem 5

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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

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