Question

Cube of even number is a ________number
A. Even
B. Odd
C. Negative
D. Prime

Answer 1

Hint: In this question we are asked to find a cube of even numbers. In order to proceed with this question we need to be clear of the terms used. The Number of a number can be calculated by multiplying the number by itself three times. Even number is the number which is a multiple of $2$. Odd number is the number which is not a multiple of$2$. Negative number is a number which is less than $0$. Prime number is a number which has only two factors- $1$ and the number itself.

Formula used: ${a^3} = a \times a \times a$

Complete step by step answer:
We are given,
A cube of even number
Let us take two examples of any random even number,
$2\;and\;12$
Now, find their cubes
${a^3} = a \times a \times a$
$
   \Rightarrow {2^3} = 8 \\
   \Rightarrow {12^3} = 1728 \\
 $
After observing both the values that we obtained in the above step, we can conclude that the cube of even numbers is always even. So, option (A) is the correct option.
When we check the same for negative even number
$ \Rightarrow - {2^3} = - 8$
The value is negative only when we find a cube of any negative even number, so option (c) is also correct, but only partially. Since it is not true in all the cases, this option is eliminated.

Note: Squares and cubes of odd numbers always result in odd numbers. Squares and cubes of even numbers always result in even numbers. While calculating the cube of any number, we need to keep in mind the sign of the term as well. Sign of the term is also multiplied three times along with the number.