Just like in base 10, you get the higher digit numbers by adding multiples of powers of the base. For example, if I write a four-digit number in base 10: [math]3652=3\cdot 10^3 + 6\cdot 10^2 + 5\cdot 10 + 2. read more
Since base 4 only uses the digits 0, 1, 2, and 3, then the largets four-digit number in base-4 is "3333". In base 10, this has a value of: 3*(4^3) + 3*(4^2) + 3*(4^1) + 3*(4^0) You could calculate this out, OR just make use of the fact that one more than this number would be "10000" in base 4. So you could just subtract 1 from 4^4. read more
In base 8, the largest number is 7777. It is equivalent to 4095 in decimal. The perfect square it is close to is 4096 = 64x64 and 3969 = 63x63. 4096 = 10000 in base 8 which is 5 digit number and 3969 = 7601 So the greatest four digit number which is a perfect square is 7601. read more