Answer
$17\sqrt {2} - 28\sqrt {3}$
Work Step by Step
Rewrite each radicand as the product of a perfect square and another factor:
$4\sqrt {9 • 2} + 5\sqrt {2} - 8\sqrt {25 • 3} + 3\sqrt {16 • 3}$
Take the square root of the perfect squares:
$4 • 3\sqrt {2} + 5\sqrt {2} - 8 • 5\sqrt {3} + 3 • 4\sqrt {3}$
Simplify the radicals by multiplying the coefficients of each radical:
$12\sqrt {2} + 5\sqrt {2} - 40\sqrt {3} + 12\sqrt {3}$
Combine like terms:
$17\sqrt {2} - 28\sqrt {3}$
