Chapter 8 - Section 8.1 - Solving Quadratic Equations by Completing the Square - Exercise Set - Page 484: 87

$-1$

Using the properties of radicals, the given expression, $ \dfrac{1}{2}-\sqrt[]{\dfrac{9}{4}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{1}{2}-\sqrt[]{\left( \dfrac{3}{2} \right)^2} \\\\= \dfrac{1}{2}-\dfrac{3}{2} \\\\= \dfrac{1-3}{2} \\\\= \dfrac{-2}{2} \\\\= -1 .\end{array}