A six digit perfect square is represented as AABCAB where the same letter represents the same digit, but a different letter represents a different digit.
It is also known that both these relationships are simultaneously satisfied:

• The numbers represented by each of AAB and CAB is a perfect square.
• The numbers represented by each of AB and ABC is a perfect square.

Determine the digits represented by A, B, and C.

Note: Computer program solutions are welcome, but a semi-analytic(calculator+ p&p) method is preferred.