Question

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Answer 1

${\large{\overbrace{\underbrace{\purple{your \: answer:1) 6 + 3 \sqrt{2} + 2 \sqrt{3} + \sqrt{6} \: 2)0}}}}}$

$\huge\red{ (3 + \sqrt{3} )(2 + \sqrt{2} )} \\ \\ \bf\purple{ \leadsto:3 \times 2 + 3 \times \sqrt{2} + \sqrt{3} \times 2 + \sqrt{3} \times \sqrt{2} } \\ \\ \bf\boxed{{ \leadsto: 6 + 3 \sqrt{2} + 2 \sqrt{3} + \sqrt{6}} } \\ \\ \huge\pink{ (3 + \sqrt{3} )(3 - \sqrt{3} ) } \\ \\ \bf\blue{ \leadsto:3 \times 3 - 3 \times \sqrt{3} + 3 \times \sqrt{3} - \sqrt{3} \times \sqrt{3} } \\ \\ \bf\blue{ \leadsto:9 \cancel{ - 3 \sqrt{3}} \cancel{+ 3 \sqrt{3}} - \sqrt{3} \times \sqrt{3} } \\ \\ \bf\blue{ \leadsto: \cancel{ + 9 } \cancel{- 9}} \\ \\ { \boxed{\blue{{ \leadsto: 0}}}}$

$\large\boxed{ \fcolorbox{pink}{red}{hope \: it \: help \: you}}$

Answer 2

Aɴꜱᴡᴇʀ

$\huge \sf{}1)6 + 3 \sqrt{2 } + 2 \sqrt{3} + 6 \\ \\ \huge \sf{}2)6$

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Gɪᴠᴇɴ

$( \sf{}3 + \sqrt{3} \: )(2 + \sqrt{2} ) \\ \sf (3 + \sqrt{3} )(3 - \sqrt{3} )$

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Tᴏ ꜰɪɴᴅ

Their simplified form

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Sᴛᴇᴘꜱ

$\sf{}first \: lets \: find \: the \: answer \: for \: the \: first \: one \\ \\ \sf{} = (3 + \sqrt{3} )(2 + \sqrt{2} ) \\ \\ \sf{} = 3 (2 + \sqrt{2} ) + \sqrt{3} (2 + \sqrt{2} ) \\ \\ \sf{} \bf = 6 + 3 \sqrt{2} + 2 \sqrt{3} + \sqrt{6}$

$\sf{}now \: for \: the \: second \: one \: if \: we \: observe \: carefully \: we \: see \: that \: \\ \\ \sf{}we \: \: can \: use \: the \: identity = (x + y)(x - y) = {x }^{2} - {y}^{2} \\ \\ \sf{}so \: substituting \:t he \: x = 3 \: and \: y = \sqrt{3} \\ \\ \sf{} \: we \: get \: ( {3}^{2} - { (\sqrt{3} )}^{2} ) \\ \\ \sf \bf{}9 - 3 = 6$

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$\huge{\mathfrak{\purple{hope\; it \;helps}}}$