# How do you simplify (5 sqrt 2 + sqrt 3)(sqrt 2 + 2 sqrt 3)?

May 16, 2018

$16 + 11 \sqrt{6}$
$\left(5 \sqrt{2} + \sqrt{3}\right) \cdot \left(\sqrt{2} + 2 \sqrt{3}\right) =$
$\left(5 \sqrt{2} \cdot \sqrt{2} + 5 \sqrt{2} \cdot 2 \sqrt{3} + \sqrt{3} \cdot \sqrt{2} + \sqrt{3} \cdot 2 \sqrt{3}\right) =$
$\left(5 \cdot 2 + 10 \sqrt{6} + \sqrt{6} + 2 \cdot 3\right) =$
$\left(10 + 11 \sqrt{6} + 6\right) =$
$16 + 11 \sqrt{6}$