Elementary Algebra

$\dfrac{3\sqrt{3}}{2y}$
Using the properties of radicals, the given expression, $\sqrt{\dfrac{27}{4y^2}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{\dfrac{9}{4y^2}\cdot3} \\\\= \sqrt{\left( \dfrac{3}{2y} \right)^2\cdot3} \\\\= \dfrac{3}{2y}\sqrt{3} \\\\= \dfrac{3\sqrt{3}}{2y} .\end{array} Note that all variables are assumed to represent positive real numbers.