3+3 #160;2+22=3+3 #160;22+22+2 #215;22=3+3 #160;4+2+42=3+3 #160;6+42 =3 #215;6+3 #215;42+3 #215;6+3 #215;42=18+122+63+46 ...

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Multiplication of Numbers

Simplify 3+32...

Question

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

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Solution

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

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

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