Find the length of side x in simplest radical form with a rational denominator

Answer:
[tex] x = \sqrt{2} [/tex]
Step-by-step explanation:
[tex] \tan 30 \degree = \frac{x}{ \sqrt{6} } \\ \\ \frac{1}{ \sqrt{3} } = \frac{x}{ \sqrt{6} } \\ \\ x = \frac{ \sqrt{6} }{ \sqrt{3} } \\ \\ x = \frac{ \: \sqrt{3} \times \sqrt{2} }{ \sqrt{3} } \\ \\ x = \sqrt{2} [/tex]