Question

"Would you classify 169 as a perfect square, perfect cube, both, or neither?

A. The number is a perfect cube because = 169.
B. The number is a perfect square because = 169.
C. The number is both a perfect square and a perfect cube because = 169 and x = 169
D. The number is neither a perfect square nor a perfect cube because there is no integer that can be squared to get 169 and no integer that can be cubed to get 169.

Answer 1

The number 169 is a perfect square because it is the square of the integer 13. It is not a perfect cube, as there is no integer that can be cubed to get 169. The correct answer choice would be "The number is a perfect square because 13×13 equals 169."

Step-by-step explanation:

To classify the number 169 as a perfect square, perfect cube, both, or neither, we should consider what these terms mean. A perfect square is a number that is the square of an integer. That is, it can be expressed as the integer multiplied by itself. In contrast, a perfect cube is a number that is the cube of an integer, which means it is the integer multiplied by itself twice.

For 169 to be a perfect square, there must be an integer whose square is 169. Indeed, 13×13 equals 169, so 169 is a perfect square. On the other hand, for 169 to be a perfect cube, there must be an integer whose cube (the integer multiplied by itself and again by itself) equals 169, which there is not. Therefore, 169 is not a perfect cube.

The correct classification of the number 169 is a perfect square, as it is the square of 13, but it is not a perfect cube.