# How do you simplify ( sqrt[6] + 2 sqrt [2] ) ( 4 sqrt[6] - 3 sqrt[2] )?

$\left(\sqrt{6} + 2 \sqrt{2}\right) \left(4 \sqrt{6} - 3 \sqrt{2}\right)$
$= \sqrt{6} \times 4 \sqrt{6} + \left(- \sqrt{6} \times 3 \sqrt{2} + 2 \sqrt{2} \times 4 \sqrt{6}\right) - 2 \sqrt{2} \times 3 \sqrt{2}$
$= 24 + \left(10 \sqrt{3}\right) - 12 = 12 + 10 \sqrt{3}$