## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$\sqrt[]{a}+12a\sqrt[]{a}$
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.