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

Which choice is equivalent to the product below when x>0? 3 x-example-1
User Tetranz
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1 Answer

4 votes

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

User Raman Mishra
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