Simplify the following expressions:
$(3+\sqrt{3})(2+\sqrt{2})$

By using identity $(a+b)(c+d)=ac+ad+bc+bd$

$(3+\sqrt{3})(2+\sqrt{2})$

$=3\times 2+\sqrt{3}\times 2+3\sqrt{2}+\sqrt{3}\times \sqrt{2}$

$=6+2\sqrt{3}+3\sqrt{2}+\sqrt{6}$