Given that
find the sum of the digits of the exact value of
Notes:
Exact value means that no rounding occurs while calculating, so the exact value of is , not or .
The sum of the digits of a number includes the digits of any decimal places, so the sum of the digits of would be .
This problem is part of the set Yay for 2014! .
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( 2 0 1 4 2 0 1 4 . 2 0 1 4 ) 2 = 2 0 1 4 2 ( 1 0 0 0 1 . 0 0 0 1 ) 2 = 4 0 5 6 1 9 6 × ( 1 0 0 0 2 0 0 0 3 . 0 0 0 2 0 0 0 1 )
It can be easily multiplied now to get the answer.