Which of the following is not a perfect square?(171)8(14,641)8(61)8(57)8

To determine which of the given numbers is not a perfect square, we need to find the square root of each number. If the square root is not a whole number, then the number is not a perfect square.

The numbers are given in base 8 (octal), so we need to convert them to base 10 (decimal) first.

1. (171)8 = 18^2 + 78^1 + 1*8^0 = 64 + 56 + 1 = 121 in decimal. The square root of 121 is 11, so (171)8 is a perfect square.

2. (14641)8 = 18^4 + 48^3 + 68^2 + 48^1 + 1*8^0 = 4096 + 2048 + 384 + 32 + 1 = 6561 in decimal. The square root of 6561 is 81, so (14641)8 is a perfect square.

3. (61)8 = 68^1 + 18^0 = 48 + 1 = 49 in decimal. The square root of 49 is 7, so (61)8 is a perfect square.

4. (57)8 = 58^1 + 78^0 = 40 + 7 = 47 in decimal. The square root of 47 is approximately 6.8556546004, which is not a whole number. Therefore, (57)8 is not a perfect square.

So, the number that is not a perfect square is (57)8.