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Answer 1

7

$\sqrt{2}\left(\sqrt{8}+2\sqrt{6}\right)-\sqrt{3}\left(\sqrt{27}+3\sqrt{6}\right)\\\\\sqrt{2}\left(2\sqrt{2}+2\sqrt{6}\right)-\sqrt{3}\left(3\sqrt{6}+\sqrt{27}\right)\\\\\sqrt{2}\left(2\sqrt{2}+2\sqrt{6}\right)-\sqrt{3}\left(3\sqrt{3}+3\sqrt{6}\right)\\\\4+4\sqrt{3}-\sqrt{3}\left(3\sqrt{3}+3\sqrt{6}\right)\\\\4+4\sqrt{3}-9-9\sqrt{2}\\\\=4\sqrt{3}-5-9\sqrt{2}$

8

A Falsa.

$\frac{3\sqrt{12}}{2}\\\\\frac{3\cdot \:2\sqrt{3}}{2}\\\\=3\sqrt{3}$

B Verdadeira.

$\left(2\sqrt{3}\right)^{-1}\\\\\frac{\sqrt{3}}{2\cdot \:3}\\\\=\frac{\sqrt{3}}{6}$

C Falsa.

$\left(2^4\right)^{\left(\frac{1}{2}\right)}\\\\2^2\\\\=4$

Portanto, alternativa B.