Answer
$4x^2y\sqrt {3xy}$
Work Step by Step
Rewrite each radicand as the product of two factors such that you can take the square root or the cube root of one of the factors, depending on the index:
$\sqrt {3^2 • 3 • x^2 • x^2 • x • y^2 • y} + \sqrt[3] {3^3 • x^3 • x^2 • y^3} - 3xy\sqrt [3] {x^2} + xy\sqrt {3 • x^2 • x • y}$
Take the square root or the cube root of the terms, depending on the index, to take them out from under the radical sign:
$3 • x • x • y\sqrt {3xy} + 3 • x • y\sqrt[3] {x^2} - 3xy\sqrt [3] {x^2} + xy • x\sqrt {3xy}$
Multiply the coefficients of each radical:
$3x^2y\sqrt {3xy} + 3xy\sqrt[3] {x^2} - 3xy\sqrt [3] {x^2} + x^2y\sqrt {3xy}$
Combine like terms. Remember that like terms are those that have the same radical and the same index:
$4x^2y\sqrt {3xy}$
