Simplify

Question:

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

 

Solution:

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

$=(3+\sqrt{3})\left[2^{2}+(\sqrt{2})^{2}+2 \times 2 \sqrt{2}\right]$

$=(3+\sqrt{3})[4+2+4 \sqrt{2}]$

$=(3+\sqrt{3})[6+4 \sqrt{2}]$

$=3 \times 6+3 \times 4 \sqrt{2}+\sqrt{3} \times 6+\sqrt{3} \times 4 \sqrt{2}$

$=18+12 \sqrt{2}+6 \sqrt{3}+4 \sqrt{6}$

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