Question

Which choice is equivalent to the product below when x>0? 3 x

Answer 1

Given:

`\sqrt[]{(3x)/(2)}\cdot\sqrt[]{(x)/(6)}`

To determine the equivalent to the product when x>0, we apply multiplication distribution property as shown below:

`(xy)^a=x^ay^a`

So,

`\begin{gathered} \sqrt[]{(3x)/(2)}\cdot\sqrt[]{(x)/(6)} \\ =\frac{\sqrt[]{3}\sqrt[]{x}}{\sqrt[]{2}}\cdot\frac{\sqrt[]{x}}{\sqrt[]{6}} \\ \text{Simplify} \\ =\frac{\sqrt[]{3}\sqrt[]{x}\sqrt[]{x}}{\sqrt[]{2}\sqrt[]{6}} \\ =\frac{\sqrt[]{3}x}{\sqrt[]{2(6)}} \\ =\frac{\sqrt[]{3}x}{\sqrt[]{12}} \\ =\frac{\sqrt[]{3}x}{2\sqrt[]{3}} \\ =(x)/(2) \end{gathered}`

Therefore, the answer is:

C. x/2