Question

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

 

Answer 1

Let us consider a number n. Then its cube would be \[n^3\] .

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

\[\left( 3n \right)^3 = 3^3 \times n^3 = 27 n^3\]

It is evident that the cube of 3n is 27 times of the cube of n.
Hence, the statement is proved.