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Answer :
Final answer:
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."
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.
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