Math is Radical!

Algebra Level 4

1046+46810+14415+2006=a2+b3+c5\sqrt{104\sqrt{6}+468\sqrt{10}+144\sqrt{15}+2006} = a\sqrt{2}+b\sqrt{3}+c\sqrt{5} where a,b,a, b, and cc are positive integers. Find abcabc.

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