Using surd forms, evaluate; \( \frac{3 \tan 60^{\circ}-2 \cos 30^{\circ}}{\tan 30^{\circ}} \)

First, let's evaluate the trigonometric values using their surd forms: - \( \tan 60^{\circ} = \sqrt{3} \) - \( \cos 30^{\circ} = \frac{\sqrt{3}}{2} \) - \( \tan 30^{\circ} = \frac{1}{\sqrt{3}} \) Now, substituting these values into the expression: \[ \frac{3 \tan 60^{\circ}-2 \cos 30^{\circ}}{\tan 30^{\circ}} = \frac{3\sqrt{3} - 2 \cdot \frac{\sqrt{3}}{2}}{\frac{1}{\sqrt{3}}} \] This simplifies to: \[ = \frac{3\sqrt{3} - \sqrt{3}}{\frac{1}{\sqrt{3}}} = \frac{2\sqrt{3}}{\frac{1}{\sqrt{3}}} \] To divide by a fraction, we multiply by its reciprocal: \[ = 2\sqrt{3} \cdot \sqrt{3} = 2 \cdot 3 = 6 \] Thus, the evaluated expression is: \[ 6 \]