Yay for 2014! #2

Algebra Level 5

Given that

201 4 2 = 4056196 2014^{2} = 4056196

find the sum of the digits of the exact value of

( 20142014.2014 ) 2 (20142014.2014)^{2}

Notes:

Exact value means that no rounding occurs while calculating, so the exact value of ( 2.1 ) 2 (2.1)^{2} is 4.41 4.41 , not 4.4 4.4 or 4 4 .

The sum of the digits of a number includes the digits of any decimal places, so the sum of the digits of 4.41 4.41 would be 4 + 4 + 1 = 9 4 + 4 + 1 = 9 .

This problem is part of the set Yay for 2014! .


The answer is 117.

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1 solution

Pranjal Jain
Dec 4, 2014

( 20142014.2014 ) 2 (20142014.2014)^{2} = 201 4 2 ( 10001.0001 ) 2 =2014^{2}(10001.0001)^{2} = 4056196 × ( 100020003.00020001 ) =4056196×(100020003.00020001)

It can be easily multiplied now to get the answer.

yes.. did it in the same way.. nice!!

Raushan Sharma - 6 years, 3 months ago

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