Question

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

Answer 1

Given expression is $(3+\sqrt{3})(2+\sqrt{2})$.

We know that, $(a+\sqrt{b})(c+\sqrt{d})=ac+a\sqrt{d}+c\sqrt{b}+\sqrt{bd}$

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

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

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

Hence, $(3+\sqrt{3})(2+\sqrt{2})=6+3\sqrt{2}+2\sqrt{3}+\sqrt{6}$