Question

prove that if a number is tripled then its cube is 27 times the cube of the given number

Answer 1

let number be x
triple of number is 3x
cube of triple is(3x)^3
then it becomes 27 x^3
therefore number is 27 times of (number that is x)^3

Answer 2

Answer:

Let the given number be x.

The cube of the given number = ( x )³ = x³

Now, the tripled number = 3 × x = 3x

Now, from given condition,

∴ ( 3x )³ = 27x³

Now, from second condition,

( 3x )³ = 27x³

Hence Proved!

Now, we will see if our proof is right or not.

Let assume that x = 2.

∴ From the first condition,

( 3 × 2 )³ = ( 6 )³ = 216 ...... ( 1 )

And now, from second condition,

27 × ( 2 )³ = 27 × 8 = 216 ........... ( 2 )

From equations ( 1 ) & ( 2 ), we can say that our proof is correct.

Hence,

If a number is tripled then its cube is 27 times the cube of the given number.

★ Some Interesting Facts ★

If we multiplied a number by another number and then we powered it ( index ) to that another number, we will get that power to the multiplied the given number.

Let's see here :

If we doubled a number then its square is 4 times the square of the given number.

Let the number be 3.

∴ From first condition,

∴ (2 × 3)² = ( 6 )² = 36 ...... ( 1 )

From second condition,

∴ 4 × ( 3 )² = 4 × 9 = 36 ....... ( 2 )

So, from ( 1 ) & ( 2 ), we can conclude the above fact.