Prove that if a number is trebled then its cube is 27

Question:

Prove that if a number is trebled then its cube is 27 times the cube of the given number.

Solution:

Let us consider a number $n$. Then its cube would be $n^{3}$.

If the number $n$ is trebled, i.e., $3 n$, we get:

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

It is evident that the cube of 3n is 27 times of the cube of n.

Hence, the statement is proved.

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