Mathematics

Problem

Simplify the following expression and write the final answer with each radical in its simplest form. Assume

x,y\ge0

. a. (i) Simplify

\sqrt{48x^{3}y^{2}}

. b. (ii) Simplify

\sqrt[3]{54x^{5}y}

. c. (iii) Hence, simplify the product

\sqrt{48x^{3}y^{2}}\times\sqrt[3]{54x^{5}y}

and express the result as a single coefficient followed by the simplest possible radical.