If x is a positive integer, for how many different values of x is \sqrt{\frac{48}{x}} a whole number?

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.