## Elementary Algebra

$10xy\sqrt[]{3}$
Using the properties of radicals, the given expression, $5\sqrt[]{12x^2y^2} ,$ simplifies to \begin{array}{l}\require{cancel} 5\sqrt[]{4x^2y^2\cdot3} \\\\= 5\sqrt[]{(2xy)^2\cdot3} \\\\= 5\cdot2xy\sqrt[]{3} \\\\= 10xy\sqrt[]{3} .\end{array} Note that all of the variables are assumed to represent non-negative real numbers.