would you classify the number 169 as a perfect square , a perfect cube, both, or neither?

A perfect square is a number that can be expressed as the product of two equal integers.

169 = 13 * 13

A perfect cube is a number that can be expressed as the product of three equal integers.


169 = 5.5287748 * 5.5287748 * 5.5287748

5.5287748 isn't whole number

so

169 is a perfect square.

PERFECT SQUIRKLE

So its a perfect square?

Perfect square

It be a perfect square.

To determine whether the number 169 is a perfect square, a perfect cube, both, or neither, we need to understand the concepts of perfect squares and perfect cubes.

A perfect square is a number that can be expressed as the square of an integer. For example, 25 is a perfect square because it can be expressed as 5^2 (5 squared). To find out if a number is a perfect square, we take the square root of the number and check if it is an integer. If the square root is an integer, then the number is a perfect square.

On the other hand, a perfect cube is a number that can be expressed as the cube of an integer. For example, 8 is a perfect cube because it can be expressed as 2^3 (2 cubed). To determine if a number is a perfect cube, we take the cube root of the number and check if it is an integer. If the cube root is an integer, then the number is a perfect cube.

Now, let's apply this knowledge to the number 169:

1. Check if 169 is a perfect square:
The square root of 169 is √169 = 13. Since 13 is an integer, we can say that 169 is a perfect square.

2. Check if 169 is a perfect cube:
The cube root of 169 is ∛169 ≈ 5.12. Since 5.12 is not an integer, we can conclude that 169 is not a perfect cube.

Therefore, the number 169 is a perfect square but not a perfect cube.

wait but aint 169 a perfect cube?