Question

The units digit of a perfect square is 6. What are the possible values of the tens digit?

Answer 1

I would play around with the numbers...
like we know 4^2=16 and 6^2=36
what is 14^2, 16^2, 24^2,...
what are the tens digits in each of those ...

Answer 2

x^2=6 mod 10
thus x=4,6 mod 10
thus x=4+10k or 6+10k
thus x^2=(4+10k)^2 or (6+10k)^2
find x^2 mod 100