Question

An odd cube number will have a/an ___ cube root.

• A. odd
• B. even
• C. fraction
• D. none of these

Answer 1

Answer: (A)

odd

We know, a cube of an even number ($\text{applicable to any multiple of an even number}$) will always be even.
Then, cube root of an odd number can never be even.

This rules out option $B$.

We also know, there are perfect cubes which are odd numbers ($27,125,343$, etc.)
Therefore, not all odd cube number need to be a fraction.

This rules out option $C$.

We know, when $2$ or more odd numbers are multiplied, the resulting number will always be odd.
Then, any cube of an odd number will also given an odd number.
Therefore, any odd perfect cube will always have a $\text{odd}$ cube root.

Hence, option $A$ is correct.