is the last one rounded?? should be 12.121??

J.R. I believe that 4 is correct. It translates to 50/8, which is 6.25 in base 10. In base 4, that equals 12.1, as the number behind the decimal is 1/4.

However, I think #3 should be '41^0.3=5', since (presumably) you're trying to take the square root of 41. In base 6, 0.5 is 5/6, and 25^(5/6) is not a rational number in any base.

Please correct me if I'm wrong on this, as it's been a while since I've dealt with base 6 decimals. :-)

J.R.! Menzinger.. No, it is 12.1 only.
James, I will correct , it is 41^0.5

James
#3 , assume base is b. and convert to decimal and square on both sides and you will get correct base system.

Ok! I understand... ;-)

The hint: use rationals.