$\left(\dfrac{5\sqrt3 - 3\sqrt5}{\sqrt5 - \sqrt3} +\dfrac{12}{\sqrt{15} + 3}\right)\sqrt{19 + 4\sqrt{15}}$
$= \left(\dfrac{\sqrt5.\sqrt5.\sqrt3 - \sqrt3.\sqrt3.\sqrt5}{\sqrt5 - \sqrt3} +\dfrac{4\sqrt3.\sqrt3}{\sqrt3.\sqrt{5} + \sqrt3.\sqrt3}\right)\sqrt{15 + 2.2\sqrt{15} + 4}$
$= \left(\dfrac{\sqrt5.\sqrt3(\sqrt5 - \sqrt3)}{\sqrt5 - \sqrt3} +\dfrac{4\sqrt3.\sqrt3}{\sqrt3(\sqrt{5} + \sqrt3)}\right)\sqrt{(\sqrt{15} + 2)^2}$
$= \left(\sqrt{15} + \dfrac{4\sqrt3}{\sqrt5 +\sqrt3}\right)(\sqrt{15} + 2)$
$= \left(\sqrt{15} + \dfrac{4\sqrt3(\sqrt5 -\sqrt3)}{5-3}\right)(\sqrt{15} + 2)$
$=(\sqrt{15} +2\sqrt3(\sqrt5 -\sqrt3))(\sqrt{15} +2)$
$= (3\sqrt{15} - 6)(\sqrt{15}+2)$
$= 3(\sqrt{15} -2)(\sqrt{15} +2)$
$= 3(15 - 4)$
$= 3.11 = 33$
