Question

becomes a perfect cube.
Prove that if a number is doubled, then its cube is 8 times the cube of the given number​

Answer 1

suppose a number is n

cube of n = n³

double of the number = 2n

cube of 2n = (2n)³ = 2³*n³

= 2*2*2n³ = 8n³

n³ is the cube of original number

Therefore, 8n³ = 8*(Cube of original number)

Answer 2

Answer:

To prove: If a number is doubled then its cube is 8 times the cube of the given number.

Proof: Let the number be 'a'

The double of the number = 2a

Cube of the number = a3

According to the given problem, 

Cube of 2a (double of the number) = ( 2a)3 

                                                        = 8 a3 

                                                        = 8 x ( cube of the  number )

                                                        = 8 times the cube of the number

Hence Proved.