Answer
$26xy\sqrt {3xy} + 4\sqrt {3y}$
Work Step by Step
First, we have to make sure that the indices are the same, which they are, in this exercise.
Then, we rewrite each radicand as the product of a perfect square and another factor:
$5x\sqrt {3x • y^2 • y} + 7\sqrt {3^2 • 3 • x^2 • x • y^2 • y} + 4\sqrt {3y}$
Take the square root of the perfect squares:
$5xy\sqrt {3xy} + 7 • 3xy\sqrt {3xy} + 4\sqrt {3y}$
Simplify the radicals by multiplying the coefficients of each radical:
$5xy\sqrt {3xy} + 21xy\sqrt {3xy} + 4\sqrt {3y}$
Combine like terms:
$26xy\sqrt {3xy} + 4\sqrt {3y}$
