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Radicals and Exponents Identify the choices that best completes the questions 3.

Radicals and Exponents Identify the choices that best completes the questions 3.-example-1
User Cookyt
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3.- Notice that:


\sqrt[]{12}=\sqrt[]{4\cdot3}=2\sqrt[]{3}\text{.}

Therefore, we can rewrite the given equation as follows:


2\sqrt[]{3}x-3\sqrt[]{3}x+5=4.

Adding like terms we get:


-\sqrt[]{3}x+5=4.

Subtracting 5 from the above equation we get:


\begin{gathered} -\sqrt[]{3}x+5-5=4-5, \\ -\sqrt[]{3}x=-1. \end{gathered}

Dividing the above equation by -√3 we get:


\begin{gathered} \frac{-\sqrt[]{3}x}{-\sqrt[]{3}}=\frac{-1}{-\sqrt[]{3}}, \\ x=\frac{1}{\sqrt[]{3}}\text{.} \end{gathered}

Finally, recall that:


\frac{1}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{3}\text{.}

Therefore:


x=\frac{\sqrt[]{3}}{3}\text{.}

Answer: Option C.

User Jiehfeng
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