 # What happens to the cube of a number if the number is multiplied by `
Question:

What happens to the cube of a number if the number is multiplied by

(i) 3?

(ii) 4?

(iii) 5?

Solution:

(i)

Let us consider a number $n$. Its cube would be $n^{3}$. If $n$ is multiplied by 3 , it becomes $3 n$.

Let us now find the cube of 3nwe get:

$(3 n)^{3}=3^{3} \times n^{3}=27 n^{3}$

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 $4 n$.

Let us now find the cube of 4nwe get:

$(4 n)^{3}=4^{3} \times n^{3}=64 n^{3}$

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 $5 n$.

Let us now find the cube of 4nwe get:

$(5 n)^{3}=5^{3} \times n^{3}=125 n^{3}$

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.