Respuesta :

Answer:

[tex]\frac{4}{3}{\sqrt3}[/tex]

Step-by-step explanation:

The question seem incomplete;

The full question is

Which expression is equivalent to 4√6/3√2

Given

4√6/3√2

Required

Find equivalent

[tex]4\sqrt6/3\sqrt2[/tex]

Rewrite Expression

[tex]\frac{4\sqrt6}{3\sqrt2}[/tex]

Expand the above expression

[tex]\frac{4\ *\ \sqrt6}{3\ * \ \sqrt2}[/tex]

Further split the fraction

[tex]\frac{4}{3}\ *\ \frac{\sqrt6}{\sqrt2}[/tex]

Using rule of surds;

[tex]\frac{\sqrt a}{\sqrt b} = \sqrt{\frac{a}{b}}[/tex]

So, the above expression becomes

[tex]\frac{4}{3}\ *\ \sqrt{\frac{6}{2}}[/tex]

[tex]\frac{4}{3}\ *\ {\sqrt3}[/tex]

[tex]\frac{4}{3}{\sqrt3}[/tex]

At this stage, the expression cannot be further simplified;

Hence, 4√6/3√2  = [tex]\frac{4}{3}{\sqrt3}[/tex]