Question

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

Answer 1

Step-by-step explanation:

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

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

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

$\sqrt{\red{3} } \times \sqrt{\red{3} } = {\red3}$

$⟹3 \sqrt{3} \times 2 \sqrt{3} + 3 \sqrt{3} \times 3 \sqrt{2} = 18 + 9 \sqrt{3} \sqrt{2}$

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

Add both terms together:-

$⟹18 + 9 \sqrt{3} \sqrt{2} + 12 + 6 \sqrt{3} \sqrt{2}$

$⟹30 + 15 \sqrt{3} \sqrt{2} =15(2 + \sqrt{3} \sqrt{2})$

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Answer 2

According to the question

$⟹(3 \sqrt{3} + 2 \sqrt{3} )(2 \sqrt{ 3} + 3 \sqrt{2} ) \\ \\ </p><p></p><p>⟹3 \sqrt{3} (2 \sqrt{3} + 3 \sqrt{2} ) + 2 \sqrt{3} (2 \sqrt{3} + 3 \sqrt{2} ) \\ \\ </p><p></p><p>\sqrt{\red{3} } \times \sqrt{\red{3} } = {\red3} \\ \\ </p><p></p><p>⟹3 \sqrt{3} \times 2 \sqrt{3} + 3 \sqrt{3} \times 3 \sqrt{2} = 18 + 9 \sqrt{3} \sqrt{2} \\ \\ </p><p></p><p>⟹2 \sqrt{3} \times 2 \sqrt{3} + 2 \sqrt{3} \times 3 \sqrt{2} = 12 + 6 \sqrt{3} \sqrt{2} \\ \\ </p><p></p><p>Add\: both\: terms\: together\::- \\ \\ </p><p></p><p>⟹18 + 9 \sqrt{3} \sqrt{2} + 12 + 6 \sqrt{3} \sqrt{2} \\ \\ </p><p></p><p>⟹30 + 15 \sqrt{3} \sqrt{2} =15(2 + \sqrt{3} \sqrt{2}) \\ \\ </p><p></p><p>$