Question

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

Answer 1

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.