Question

Prove that if a number is tripled , then it's cube is 27 times the cube of the given number ?

Answer 1

Answer:

Let the given number be x,

then, triple of given number=3x

cube of triple of given number=(3x)^3=3^3 ×x^3=27 × x^3

now,

cube of given number=x^3

27 times of cube of given number=27 × x^3

hence,

cube of triple of given number=27 times of cube of given number(hence proved)

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.