Answer
$\sqrt[]{a}+12a\sqrt[]{a}$
Work Step by Step
Simplifying each term and then combining like terms, the given expression, $
\sqrt[]{a}+3\sqrt[]{16a^3}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[]{a}+3\sqrt[]{16a^2\cdot a}
\\\\=
\sqrt[]{a}+3\sqrt[]{(4a)^2\cdot a}
\\\\=
\sqrt[]{a}+3\cdot4a\sqrt[]{a}
\\\\=
\sqrt[]{a}+12a\sqrt[]{a}
.\end{array}
* Note that it is assumed that all variables represent positive numbers.
