Respuesta :
Answer:
3
Step-by-step 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 [tex]\sqrt{\frac{48}{x} }[/tex] 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 [tex]\sqrt{\frac{48}{3} } = \sqrt{16}[/tex] ⇒ 4
- If, x=12, Then [tex]\sqrt{\frac{48}{12} } = \sqrt{4}[/tex] ⇒ 2
- If, x=48, Then [tex]\sqrt{\frac{48}{48} } = \sqrt{1}[/tex] ⇒ 1
Thus, There are 3 whole numbers (3,12,48).
