Hmm, interesting question.The digital root of a number is equivalent to the original number modulo 9.The digital root of N^2 depends only on the digital root of N. We list all possible situations, where d(...) stands for the digital root:d(1^2) = d(1) = 1d(2^2) = d(4) = 4d(3^2) = d(9) = 9d(4^2) = d(16) = 7d(5^2) = d(25) = 7d(6^2) = d(36) = 9d(7^2) = d(49) = 4d(8^2) = d(64) = 1d(9^2) = d(81) = 9The possible values are: 1, 4, 7 and 9.
