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

1, 3, 5, 7, 9 are the possible digits for the tens digit. Notice they are all odd.

My reasoning:

When you multiply any 2 numbers together, the last digit of the result will be the last digit of the product of the original last digits (ex. 12*7 = 84:  7*2 = 14 : 4 is last digit)

The last TWO digits of the result will be the same as the last 2 digits of the product of just the last two digits. (ex, 1422*234 = 332,748:  22*48 = 748 : 48 are last two digits )
If is a perfect square ends in 6,  the last digit squared must end in 6 as well.The only single digit numbers squared that end in 6 are:    4*4=16   and   6*6=36  They are the only 2 so the number that is being squared must end in 4 or 6Let the second last digit be X.  X can be any digit.So the last 2 digits of our number that is being squared are either   X6   or    X4That is, the last 2 digits of the number are either (10X+6)   or   (10X+4),this will result in X always being an odd number.