Answer:
The correct option is D) [tex]\frac{\sqrt{3}}{2}[/tex]
Step-by-step explanation:
We need to find out the quotient of [tex]\frac{3\sqrt{8}}{4\sqrt{6}}[/tex]
[tex]=\frac{3\sqrt{8}}{4\sqrt{6}}[/tex]
Rewrite the above expression;
[tex]=\frac{3\times2 \sqrt{2}}{4\sqrt{6}}[/tex]
[tex]=\frac{6\sqrt{2}}{4\sqrt{6}}[/tex]
Cancel out the common term from numerator and denominator,
[tex]=\frac{3\sqrt{2}}{2\sqrt{6}}[/tex]
[tex]=\frac{3\sqrt{2}}{2\sqrt{2}\times \sqrt{3}}[/tex]
[tex]=\frac{3}{2\sqrt{3}}[/tex]
Multiply numerator and denominator with [tex]\sqrt{3}[/tex]
[tex]=\frac{3\sqrt{3}}{2\sqrt{3}\sqrt{3}}[/tex]
[tex]=\frac{3\sqrt{3}}{2\times 3}[/tex]
[tex]=\frac{3\sqrt{3}}{6}[/tex]
[tex]=\frac{\sqrt{3}}{2}[/tex]
Therefore, the correct option is D) [tex]\frac{\sqrt{3}}{2}[/tex]
