Question

Is 1298 a perfect square, perfect cube or neither? Prove using prime factorization.

Answer 1

Neither

Explanation:

1298 = 2 x 11 x 59

Checking if it is a perfect square.

`√(1298) = √(2 * 11 * 59 )`

Clearly, 1298 is not a perfect square.

Checking if it is a perfect cube.

`\sqrt[3]{1298} = \sqrt[3]{2 * 11 * 59}`

Clearly, 1298 is not a perfect cube.