#### Answer

$\sqrt{3}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
\sqrt{\dfrac{12}{16}}+\sqrt{\dfrac{48}{64}}
,$ 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}
\sqrt{\dfrac{4}{16}\cdot3}+\sqrt{\dfrac{16}{64}\cdot3}
\\\\=
\sqrt{\dfrac{1}{4}\cdot3}+\sqrt{\dfrac{1}{4}\cdot3}
\\\\=
\sqrt{\left( \dfrac{1}{2} \right)^2\cdot3}+\sqrt{\left(\dfrac{1}{2}\right)^2\cdot3}
.\end{array}
Extracting the root of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\dfrac{1}{2}\sqrt{3}+\dfrac{1}{2}\sqrt{3}
\\\\=
\dfrac{\sqrt{3}}{2}+\dfrac{\sqrt{3}}{2}
.\end{array}
Combining the like radicals results to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{3}+\sqrt{3}}{2}
\\\\=
\dfrac{2\sqrt{3}}{2}
\\\\=
\dfrac{\cancel{2}\sqrt{3}}{\cancel{2}}
\\\\=
\sqrt{3}
.\end{array}