Answer :
Answer:
- 3 different values of x make the expression a whole number.
Explanation:
The fraction expression is:
[tex]\sqrt{\dfrac{48}{x}}[/tex]
You need to find the divisors of 48 that make 48/x a perfect square:
The perfect squares less than 48 are 1, 4, 9, 16, 25, and 36.
The divisors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
Only 48/3 = 16, 48/12 = 4, and 48/48 = 1 are perfect squares.
Thus, 3, 12, and 48, are the values of x that make the expression a whole number.
Those are 3 numbers.
Hence, the answer is that there are 3 different values of x that make the fraction a whole number.