Simplify: (3+3 ) (2+2 )^2 - Vidyadip

Question

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

✓

Answer

$\big(3+\sqrt{3}\big)\big(2+\sqrt{2}\big)^2$
$=\big(3+\sqrt{3}\big)\Big[(2)^2+2\times2\times\sqrt{2}+\big(\sqrt{2}\big)^2\Big]$
$=\big(3+\sqrt{3}\big)\big[4+4\sqrt{2}+2\big]$
$=\big(3+\sqrt{3}\big)\big(6+4\sqrt{2}\big)$
$=3\times6+3\times4\sqrt{2}+6\sqrt{3}+4\sqrt{2}\times\sqrt{3}$
$=18+12\sqrt{2}+6\sqrt{3}+4\sqrt{6}$

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