A, B, C are digits.
7AB = 700+ 10 A + B. Its value is between 700 and 799.
CC = 10 C + C = 11 C, C * CC = 11*C²
Given 700+ 10 A + B = 11 C²
So 700 <= 11 C² <= 799
63 <= C² <= 72
Hence, C = 8.
So 11 C² = 11 * 8² = 704
Hence, B = 4, A = 0.
A =0, B = 4, C = 8