Answer:
C
Step-by-step explanation:
using the rules of radicals
• [tex]\frac{\sqrt{a} }{\sqrt{b} }[/tex] ⇔ [tex]\sqrt{\frac{a}{b} }[/tex]
• [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
given [tex]\sqrt{27x}[/tex] ÷ [tex]\sqrt{48}[/tex]
simplifying the radicals
[tex]\sqrt{27x}[/tex] = [tex]\sqrt{9(3)x}[/tex] = 3[tex]\sqrt{3x}[/tex]
[tex]\sqrt{48}[/tex] = [tex]\sqrt{16(3)}[/tex] = 4[tex]\sqrt{3}[/tex], hence
[tex]\frac{3\sqrt{3x} }{4\sqrt{3} }[/tex]
= [tex]\frac{3\sqrt{x} }{4}[/tex] → C
