#### Answer

$\dfrac{\sqrt{3}}{2}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
\dfrac{\sqrt{27}}{2}-\dfrac{3\sqrt{3}}{2}+\dfrac{\sqrt{3}}{\sqrt{4}}
,$ find a factor of the radicand that is a perfect power of the index. Then, extract the root of that factor. Finally, combine the like radicals.
$\bf{\text{Solution Details:}}$
Rewriting the radicand with a factor that is a perfect power of the index, the given expression is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{9\cdot3}}{2}-\dfrac{3\sqrt{3}}{2}+\dfrac{\sqrt{3}}{\sqrt{4}}
\\\\=
\dfrac{\sqrt{(3)^2\cdot3}}{2}-\dfrac{3\sqrt{3}}{2}+\dfrac{\sqrt{3}}{\sqrt{(2)^2}}
.\end{array}
Extracting the root of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\dfrac{3\sqrt{3}}{2}-\dfrac{3\sqrt{3}}{2}+\dfrac{\sqrt{3}}{2}
.\end{array}
Combining the like radicals results to
\begin{array}{l}\require{cancel}
\dfrac{3\sqrt{3}-3\sqrt{3}+\sqrt{3}}{2}
\\\\=
\dfrac{\sqrt{3}}{2}
.\end{array}