## Intermediate Algebra (12th Edition)

$(4+3xy)\sqrt[3]{xy^2}$
$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $\sqrt[3]{64xy^2}+\sqrt[3]{27x^4y^5} ,$ simplify first each term by expressing the radicand as a factor that is a perfect power of the index. Then, extract the root. Finally, combine the like radicals. $\bf{\text{Solution Details:}}$ Expressing the radicand as an expression that contains a factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt[3]{64\cdot xy^2}+\sqrt[3]{27x^3y^3\cdot xy^2} \\\\= \sqrt[3]{(4)^3\cdot xy^2}+\sqrt[3]{(3xy)^3\cdot xy^2} .\end{array} Extracting the roots of the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} 4\sqrt[3]{xy^2}+3xy\sqrt[3]{xy^2} .\end{array} By combining like radicals, the expression above is equivalent to \begin{array}{l}\require{cancel} (4+3xy)\sqrt[3]{xy^2} .\end{array}