Chapter 9 - Roots and Radicals - 9.3 - More on Simplifying Radicals - Problem Set 9.3 - Page 412: 19

$\dfrac{\sqrt{6}}{2}$

Using the properties of radicals, the given expression, $ \sqrt{\dfrac{3}{2}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{\dfrac{3}{2}\cdot\dfrac{2}{2}} \\\\= \sqrt{\dfrac{6}{4}} \\\\= \dfrac{\sqrt{6}}{\sqrt{4}} \\\\= \dfrac{\sqrt{6}}{2} .\end{array}