Question

If x is a positive integer, for how many different values of x is StartRoot StartFraction 48 Over x EndFraction EndRoot a whole number? 2 3 6 10

Answer 1

bbbbbbbbbbbbbbbbb

Explanation:

Answer 2

3

Explanation:

According To the Question,

• Given that, 'x' is a positive integer . And We have to find the number of different values of 'x', So that the value of
  `\sqrt{(48)/(x) }` is a Whole number.

Then First, we have to find those values of 'x' for which the given fraction is a square.

We Know, All the factors of 48 are {1,2,3,4,6,8,12,16,24,48} .

Now, From the above factors, only (3,12 & 48) can give us a square number.

Therefore,

• If x=3, Then
  `\sqrt{(48)/(3) } = √(16)` ⇒ 4

• If, x=12, Then
  `\sqrt{(48)/(12) } = √(4)` ⇒ 2

• If, x=48, Then
  `\sqrt{(48)/(48) } = √(1)` ⇒ 1

Thus, There are 3 whole numbers (3,12,48).