Question

6. Find the smallest whole number by which each of the following numbers must be multiplied to
obtain a perfect cube
(1) 81​

Answer 1

Answer:

9 is the smallest number to be multiplied with 81 to make it a perfect cube.

Step-by-step explanation:

A number becomes a perfect cube when its prime factors are in groups of 3,

For ex:- 64

64 = 2 × 2 × 2 × 2 × 2 × 2

64 = 2³ × 2³

Since, they are in groups of 3, it is a perfect cube,

Now, according to the Question,

81 = 3 × 3 × 3 × 3

81 = 3³ × 3

Here, its prime factors are not in groups of 3, so 81 is not a perfect cube.

But to make 81 a perfect cube we must pair up with 3 to form a group of 3.

So,

If 3² is multiplied with 3 it becomes 3³, making it a perfect cube,

Let's see how,

81 = 3³ × 3

Multiplying 3²

= 3³ × 3 × 3²

= 3³ × 3³

Now, they are in groups of 3, hence, now it is a perfect cube

Hence,

3² = 9 is the smallest number to be multiplied with 81 to make it a perfect cube.

Hope it helped and believing you understood it........All the best