Respuesta :
1. We want all values of x such that [tex] \sqrt{ \frac{48}{x} } [/tex] is a whole number.
2. Fist of all, x must be a factor of 48
48=2*24=2*8*3=2*(2*2*2)*3=[tex] 2^{4}*3 [/tex]. This is called the prime factorization, so we write 48 as a multiplication of its prime factors so that we can write all the factors in an organized form without missing any.
All factors of 48 with only 2's are {2, 4, 8, 16}
All factors of 48 with 2's and 3 are {6, 12, 24, 48}
And there is 1 and 3.
3. We will check all of these factors as 48/x and see whether the division is a perfect square, so that the square of it is a hole number.
4.
48/2=24
48/4=12
48/8=6
48/16=3
48/6=8
48/12=4 a perfect square
48/24=2
48/48=1 a perfect square
48/3=16 a perfect square
so for x=12, x= 48 or x=3 , [tex] \sqrt{ \frac{48}{x} } [/tex] is a whole number.
Answer: 3 values
2. Fist of all, x must be a factor of 48
48=2*24=2*8*3=2*(2*2*2)*3=[tex] 2^{4}*3 [/tex]. This is called the prime factorization, so we write 48 as a multiplication of its prime factors so that we can write all the factors in an organized form without missing any.
All factors of 48 with only 2's are {2, 4, 8, 16}
All factors of 48 with 2's and 3 are {6, 12, 24, 48}
And there is 1 and 3.
3. We will check all of these factors as 48/x and see whether the division is a perfect square, so that the square of it is a hole number.
4.
48/2=24
48/4=12
48/8=6
48/16=3
48/6=8
48/12=4 a perfect square
48/24=2
48/48=1 a perfect square
48/3=16 a perfect square
so for x=12, x= 48 or x=3 , [tex] \sqrt{ \frac{48}{x} } [/tex] is a whole number.
Answer: 3 values
