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Perfect Square Sum

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1 Perfect Square Sum on Tue Feb 02, 2010 12:25 am


What is the first perfect square when the sum of the digits is equal to the square root?

2 Re: Perfect Square Sum on Tue Feb 02, 2010 8:23 pm


technically, 0 is the first perfect square, and the only digit is its square root, 0. this also works for 1, 2, and 3, which are all single digits, so the square of the sum of the digits is the original number. however, you said digitS, in which case there would need to be more than one digit. in that case, the first perfect square that applies is 9, because 9^2 = 81, and 8+1=9.

3 Re: Perfect Square Sum on Tue Feb 02, 2010 10:30 pm


Correct!! and good point, I forgot about zero. Two and three don't work though.

2^2 = 4 which is not 2.
3^2 = 9 which is not 3.

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