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

$24x^3\sqrt[]{5x}$
Using the properties of radicals, the given expression, $3\sqrt[]{2x^5}\cdot4\sqrt[]{10x^2} ,$ simplifies to \begin{array}{l}\require{cancel} 3(4)\sqrt[]{2x^5(10x^2)} \\\\= 12\sqrt[]{20x^7} \\\\= 12\sqrt[]{4x^6\cdot5x} \\\\= 12\sqrt[]{(2x^3)^2\cdot5x} \\\\= 12(2x^3)\sqrt[]{5x} \\\\= 24x^3\sqrt[]{5x} \end{array} * Note that it is assumed that no radicands were formed by raising negative numbers to even powers.