Since there are so few options, trial and error/enumeration would be the way to go here.
The 2-digit squares are: 16, 25, 36, 49, 64, 81, 100. The 2-digit cubes are: 27, 64.
The only place where the difference between two of these numbers is 2, occurs between 25 and 27, thus the 2-digit number asked for is 26.
26 5*5 and 3*3*3
87 is the only 2-digit number that is 6 greater and 13 less than a square, but it is not prime.
2 digit number which is square number less than 42 but greater than 29 = 36square numbers are 2, 9, 16, 25, 36, 49,...
there is no number less than 49 between 1 and 100 that if multiplied by 2 will have a 3-digit product no number less than 50, actually
26
26
26 5*5 and 3*3*3
87 is the only 2-digit number that is 6 greater and 13 less than a square, but it is not prime.
2 digit number which is square number less than 42 but greater than 29 = 36square numbers are 2, 9, 16, 25, 36, 49,...
It is: 81
the number is 24.. 24 is one less than 25 which is 5 squared when doubled its 48, which is one less than 7 squared (49)
36
there is no number less than 49 between 1 and 100 that if multiplied by 2 will have a 3-digit product no number less than 50, actually
26
something I don't know
123
The biggest number with 6 digits that is a perfect square is 999,999. When squared, it becomes 999,999,000,001.