Question

Is it true cubes of odd numbers are always odd? explain your reasoning.

Answer 1

Step 1:

For natural numbers, we know,

odd×odd=odd

odd×even=even

even×even=even.

Step 2:

So, a cube of a natural odd number is

odd×odd×odd

=odd×odd

=odd.

Step 3:

For example,

`\begin{gathered} 7\text{ }*\text{ 7 }*\text{ 7 = 343} \\ 3\text{ }*\text{ 3 }*\text{ 3 = 27} \end{gathered}`

Final answer

The cube of a natural odd number is always odd.