Question

What happens to the cube of a number if the number is multiplied by
(i) 3?
(ii) 4?
(iii) 5?

Answer 1

(i)
Let us consider a number n. Its cube would be $n^3$. If n is multiplied by 3, it becomes 3n.
Let us now find the cube of 3n, we get:
${\left(3n\right)}^3=3^3\times n^3=27n^3$
Therefore, the cube of 3n is 27 times of the cube of n.

Thus, if a number is multiplied by 3, its cube is 27 times of the cube of that number.

(ii)
Let us consider a number n. Its cube would be $n^3$. If n is multiplied by 4, it becomes 4n.
Let us now find the cube of 4n, we get:
${\left(4n\right)}^3=4^3\times n^3=64n^3$
Therefore, the cube of 4n is 64 times of the cube of n.

Thus, if a number is multiplied by 4, its cube is 64 times of the cube of that number.

(iii)
Let us consider a number n. Its cube would be $n^3$. If the number n is multiplied by 5, it becomes 5n.
Let us now find the cube of 4n, we get:
${\left(5n\right)}^3=5^3\times n^3=125n^3$
Therefore, the cube of 5n is 125 times of the cube of n.

Thus, if a number is multiplied by 5, its cube is 125 times of the cube of that number.