## College Algebra (11th Edition)

$12\sqrt{2x}$
$\bf{\text{Solution Outline:}}$ To add/subtract the given expression, $8\sqrt{2x}-\sqrt{8x}+\sqrt{72x} ,$ simplify first each radical term by extracting the factor that is a perfect power of the index. Then, combine the like radicals. $\bf{\text{Solution Details:}}$ Extracting the factors of each radicand that is a perfect power of the index results to \begin{array}{l}\require{cancel} 8\sqrt{2x}-\sqrt{4\cdot2x}+\sqrt{36\cdot2x} \\\\= 8\sqrt{2x}-\sqrt{(2)^2\cdot2x}+\sqrt{(6)^2\cdot2x} \\\\= 8\sqrt{2x}-2\sqrt{2x}+6\sqrt{2x} .\end{array} By combining the like radicals, the expression above simplifies to \begin{array}{l}\require{cancel} (8-2+6)\sqrt{2x} \\\\= 12\sqrt{2x} .\end{array}