Question

O produto
$(\sqrt{3} - \sqrt{2} ).( \sqrt{3 .\sqrt{2} } )$
é igual a?​

Answer 1

Oie, Td Bom?!

$= ( \sqrt{3} - \sqrt{2} ) \: . \: ( \sqrt{3 \sqrt{2} } )$

$= \sqrt{3} \sqrt{3 \sqrt{2} } - \sqrt{2} \sqrt{3 \sqrt{2} }$

$= \sqrt{9 \sqrt{2} } - \sqrt{6 \sqrt{2} }$

$= \sqrt{ 3{}^{2} \sqrt{2} } - \sqrt{ \sqrt{6 {}^{2} } \sqrt{2} }$

$= \sqrt{3 {}^{2} } \sqrt{ \sqrt{2} } - \sqrt{ \sqrt{6 {}^{2} } \sqrt{2} }$

$= 3 \sqrt{ \sqrt{2} } - \sqrt{ \sqrt{6 {}^{2} } \sqrt{2} }$

$= 3 \sqrt[2 \: . \: 2]{2} - \sqrt{ \sqrt{6 {}^{2} \: . \: 2 } }$

$= 3 \sqrt[4]{2} - \sqrt{ \sqrt{6 {}^{2} \: . \: 2 } }$

$= 3 \sqrt[4]{2} - \sqrt{ \sqrt{36 \: . \: 2} }$

$= 3 \sqrt[4]{2} - \sqrt{ \sqrt{72} }$

$= 3 \sqrt[4]{2} - \sqrt[2 \: . \: 2]{72}$

$= 3 \sqrt[4]{2} - \sqrt[4]{72}$

$≈0,654...$

Att. Makaveli1996

Answer 2

$(\sqrt{3}-\sqrt{2})\cdot(\sqrt{3\sqrt{2}})\\\\\sqrt{3}\sqrt{3\sqrt{2}}-\sqrt{2}\sqrt{3\sqrt{2}}\\\\\sqrt{3\cdot3\sqrt{2}}-\sqrt{2\cdot3\sqrt{2}}\\\\\sqrt{9\sqrt{2}}-\sqrt{6\sqrt{2}}$

É o máximo que da pra fazer