The Beautiful Number

There are three one digit numbers which are perfect squares (1, 4, 9) . The only two digit perfect square number which can be formed with these digits is $\boxed{49}$

The only two digits perfect square are $16,25,36,49,64,81$ . For one digit numbers, $0,1,4,9$ are perfect squares, but $2,3,5,6,7,8$ are not perfect square.

The $'6'$ inside $16$ is not perfect square. The $'2'$ inside $25$ is not perfect square. The $'3'$ inside $36$ is not perfect square. The $'6'$ inside $64$ is not perfect square. The $'8'$ inside $81$ is not perfect square. As $4,9,49$ are all perfect squares, the only answer is $\large 49$