Question

Simplify the following expression:

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

Answer 1

On simplify,

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

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

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

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

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