Question

Multiply $(3\sqrt{18}+2\sqrt{12})$ by $(\sqrt{50}-\sqrt{27})$

Answer 1

$(3\sqrt{18}+2\sqrt{12})(\sqrt{50}-\sqrt{27})$
$=(9\sqrt{2}+4\sqrt{3})(5\sqrt{2}-3\sqrt{3})$ each surd is reduced to its simplest form.
$=9\sqrt{2}(5\sqrt{2}-3\sqrt{3})+4\sqrt{3}(5\sqrt{2}-3\sqrt{3})$
$=(45\times 2)-27\sqrt{6}+20\sqrt{6}-(12\times 3)$
$=90-7\sqrt{6}-36$
$=54-7\sqrt{6}$