Question

When four times of a non zero positive number is divided by its cube root, the quotient is obtained as 36. If cube root of the number is divided by the number itself, then the resulting number is equal to

Answer 1

Solution :-

Let us assume that, the non zero positive number is x .

it is given that, when the numbers x four times that is 4x is divided by cube root of x , we will get quotient as 36 .

So,

→ 4x ÷ (x)^(1/3) = 36

→ 4x = 36 * (x)^(1/3)

→ x = 9 * (x)^(1/3)

cubing both sides , we get,

→ (x)³ = {9 * (x)^(1/3)}³

→ x³ = (9)³ * {(x)^(1/3)}³

→ x³ = (9)³ * x

→ x² = (9)³

→ (x)² = 729

→ x² = (27)²

Square - root both sides now, we get,

→ x = 27 .

Therefore,

→ cube root of the number = (27)^(1/3) = (3³)^(1/3) = 3 .

Hence,

→ Resulting Number = (cube root of the number) / (Number itself)

→ Resulting Number = 3 / 27

→ Resulting Number = (1/9) (Ans.)

Hence, the Resulting Number will be (1/9) .

Answer 2

Given:

When four times of a non zero positive number is divided by its cube root, the quotient is obtained as 36.

To find:

If the cube root of the number is divided by the number itself, then the resulting number is equal to

Solution:

From given, we have,

When four times of a non zero positive number is divided by its cube root, the quotient is obtained as 36.

Let the number be "x"

So, we get,

4x/∛x = 36

4x = 36 (∛x)

cubing on the both sides, we get,

(4x)³ = [36 (∛x)]³

64x³ = (36)³ x

64x³ = 46656 x

x² = 46656/64

x = 27

Therefore, the number is 27

Now consider,

If the cube root of the number is divided by the number itself,

= ∛27/27

= 3/27

= 1/9

Therefore, the resulting number is equal to  1/9