The expression is given as
[tex]\tan 30^{\circ}[/tex]The exact value of tan 30 is
[tex]\tan 30^{\circ}=\frac{1}{\sqrt[]{3}}[/tex]Simplify it by multiply square root 3 in denominator and numerator.
[tex]\tan 30^{\circ}=\frac{\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}}=\frac{\sqrt[]{3}}{3}[/tex]Hence the correct option is C.