Rationalize the denominator. Assume that all variables represent positive real numbers. \( \frac{1}{\sqrt{12 z}} \) \( \frac{1}{\sqrt{12 z}}=\square \) (Type an exact answer, using radicals as needed.)

To rationalize the denominator of \( \frac{1}{\sqrt{12 z}} \), multiply the numerator and the denominator by \( \sqrt{12 z} \): \[ \frac{1}{\sqrt{12 z}} \cdot \frac{\sqrt{12 z}}{\sqrt{12 z}} = \frac{\sqrt{12 z}}{12 z} \] Now, simplify \( \sqrt{12} \) to \( 2\sqrt{3} \): \[ \frac{2\sqrt{3} \sqrt{z}}{12 z} = \frac{2\sqrt{3}}{12 \sqrt{z}} = \frac{\sqrt{3}}{6 \sqrt{z}} \] So, \( \frac{1}{\sqrt{12 z}} = \frac{\sqrt{3}}{6 \sqrt{z}} \).