First, we are going to perform the division of the fraction inside the radical:
[tex] \frac{96}{8} =12[/tex]
So, we can rewrite our radical as follows:
[tex] \sqrt{ \frac{96}{8}} = \sqrt{12} [/tex]
Now, we are going to decompose 12 into prime factors:
[tex]12=2^2*3[/tex]
So, we can rewrite our fraction as follows:
[tex] \sqrt{12} = \sqrt{2^2*3} [/tex]
Since 2 has the same exponent as the index of the radical, we can take it out:
[tex]\sqrt{2^2*3}=2 \sqrt{3} [/tex]
We can conclude that the simplified form of the expression is: [tex]2 \sqrt{3}[/tex]
