Question

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

Answer 1

Hint: In this question, first we suppose a number as ‘x’. After this we will find the cube of this number. Next time we will multiply the number by 3 and then find its cube which says that the cubic value gets 27 times.

Complete step-by-step answer:

Let the number be ‘x’.

We know that the cube of a number is just the same number multiplied three times.

$\therefore $ Cube of number ‘x’ = ${{\text{x}}^3}$ (1)

Now, triple of the number = 3x.

On finding the cube of ‘3x’, we get:

Cube of ‘3x’ = ${\left( {3{\text{x}}} \right)^3} = (3{\text{x)}} \times (3{\text{x)}} \times

(3{\text{x) = 27}}{{\text{x}}^3}$. (2)

Putting the value of ‘${{\text{x}}^3}$’ in equation 2, we get:

Cube of triple of number = cube of ‘3x’ = $27 \times $ cube of the number ‘x’.

Thus it is proved that the cube of a triple of a number is 27 times the cube of the original number.


Note: In this type of question, you should know how to calculate the cube of a number. It is obtained by multiplying the given number three times. In general we can write:
${{\text{a}}^n} = {\text{a}} \times {\text{a}} \times {\text{a}} \times .... \times {\text{n times}}$, where ‘n’ is a natural number. If the number is multiplied by a number say ‘p’ then:
${\left( {{\text{pa}}} \right)^n} = ({\text{pa)(pa)(pa)}}.... \times {\text{n times = }}{{\text{p}}^n}{{\text{a}}^n}$.