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

# Perfect Square Sum

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

#### hazzmta

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 digit

**S**, 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

#### EccentricPhilosopher

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.

2^2 = 4 which is not 2.

3^2 = 9 which is not 3.

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