Question

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

Please explain step by step ​

Answer 1

Answer:

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Answer 2

Answer:

triple of the number = 3x. Putting the value of 'x3' in equation 2, we get: Cube of triple of number = cube of '3x' = 27× 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.

Step-by-step explanation:

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

∴ Cube of number ‘x’ = x3 (1)

Now, triple of the number = 3x.

On finding the cube of ‘3x’, we get:

Cube of ‘3x’ = (3x)3=(3x)×(3x)×(3x) = 27x3. (2)

Putting the value of ‘x3’ in equation 2, we get:

Cube of triple of number = cube of ‘3x’ = 27× 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:

an=a×a×a×....×n times, where ‘n’ is a natural number. If the number is multiplied by a number say ‘p’ then:

(pa)n=(pa)(pa)(pa)....×n times = pnan