If x is a positive integer, for how many different values of x is StartRoot StartFraction 48 Over x EndFraction EndRoot a whole
2 answers:
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
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
⇒ 4
- If, x=12, Then
⇒ 2
- If, x=48, Then
⇒ 1
Thus, There are 3 whole numbers (3,12,48).
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