Answer:
[tex]8\sqrt{6}[/tex]
Step-by-step explanation:
Remember that
[tex]\sqrt{a}=a^{\frac{1}{2}}[/tex]
and
[tex]\sqrt{ab}=(ab)^{\frac{1}{2}}=(a)^{\frac{1}{2}}(b)^{\frac{1}{2}}[/tex]
we have the number
[tex]\sqrt{384}[/tex]
Decompose the number in prime factors
[tex]384=2^{7}3=2^{6}(2)(3)=2^{6}(6)[/tex]
substitute
[tex]\sqrt{2^{6}(6)}=(2)^{\frac{6}{2}}(6)^{\frac{1}{2}}=2^3\sqrt{6}=8\sqrt{6}[/tex]
therefore
The expression in simplest radical form is [tex]8\sqrt{6}[/tex]
