Question

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

Answer 1

Let the number be x.
Then it's cube =x^3.
If x is tripled =3x.
cube of 3x =27x^3.
then,
27x^3/x^3=27/1
OR. 27:1
THUS it proves this ..
Hope this helps.
please hit thanks...
and mark brainliest if you wish : )

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.