## Elementary Algebra

$\dfrac{\sqrt{3}}{6}$
Recall, we are not allowed to have radicals in the denominator of a fraction. Using the properties of radicals, the given expression, $\sqrt{\dfrac{1}{12}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{\dfrac{1}{12}\cdot\dfrac{3}{3}} \\\\= \sqrt{\dfrac{3}{36}} \\\\= \dfrac{\sqrt{3}}{\sqrt{36}} \\\\= \dfrac{\sqrt{3}}{\sqrt{(6)^2}} \\\\= \dfrac{\sqrt{3}}{6} .\end{array}