Answer: [tex]2\sqrt{6x}[/tex]
Step-by-step explanation:
The expression [tex]4\sqrt{\frac{3}{2}x}[/tex] can be written as:
[tex]4(\frac{\sqrt{3x}}{\sqrt{2}})[/tex]
Therefore, to simplify the expression you need to Rationalize the denominator to get rid the radical [tex]\sqrt{2}[/tex]:
Then, you must multiply the numerator and the denominator by [tex]\sqrt{2}[/tex].
Remember the following:
[tex](\sqrt{a})^{2}=a[/tex]
Also remember that:
[tex]\sqrt[n]{a}*\sqrt[n]{b}=\sqrt[n]{ab}[/tex]
Therefore, you get:
[tex]4(\frac{(\sqrt{3x})(\sqrt{2})}{(\sqrt{2})(\sqrt{2})})=4(\frac{\sqrt{6x}}{(\sqrt{2})^2})=4(\frac{\sqrt{6x}}{2})=\frac{4\sqrt{6x}}{2}=2\sqrt{6x}[/tex]
