Question

Would you classify the number 55 as a perfect square, as a perfect cube, both, or neither?

Answer 1

Neither.

Explanation:

We are asked to classify 55.

Let us take square root of 55 to determine whether 55 is a perfect square or not.

`√(55)`

`√(55)=7.41619848\approx 7.42`

Since 7.42 is not an integer, therefore, 55 is not a perfect square.

Let us take cube root of 55 to determine whether 55 is a perfect cube or not.

`\sqrt[3]{55}`

`\sqrt[3]{55}=3.802952460\approx 3.80`

Since 3.80 is not an integer, therefore, 55 is not a perfect cube.

Therefore, 55 is neither perfect square nor perfect cube.

Answer 2

It is neither.

The list of perfect squares is {1, 4, 9, 16, 25, 36, 49, 64, ...} and you can see that 55 is not listed.

The list of perfect cubes is {1, 8, 27, 64, ...} and 55 isn't listed here either

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Note: To compute the list of perfect squares, you square the set {1,2,3,...}
So
1^2 = 1
2^2 = 4
3^2 = 9
etc etc

For the perfect cubes, we cube each value from {1,2,3...}
1^3 = 1
2^3 = 8
3^3 = 27
etc etc