Question

escreva na forma mais simples o valor de 2:$(\sqrt{\frac{\sqrt{3} }{\sqrt{3} +3} }^{2})$

Answer 1

${\sqrt{ \frac{ \sqrt{3} }{ \sqrt{3} + 3} } }^{2} = \frac{ \sqrt{3} }{ \sqrt{3} + 3} = \frac{ \sqrt{3}( \sqrt{3} - 3) }{( \sqrt{3} + 3)( \sqrt{3} - 3) }$

$\frac{ \sqrt{3}( \sqrt{3} - 3)}{ { \sqrt{3} }^{2} - {3}^{2}} = \frac{ \sqrt{3}( \sqrt{3} - 3) }{3 - 9} = - \frac{ \sqrt{3}( \sqrt{3} - 3) }{6}$

2.(-6/√3(3-√3)) =-12/(3√3-3)

= -12.(3√3+3)/(3√3-3)(3√3+3)

=-12(3√3+3)/(3√3)²-3²

=-12(3√3+3)/(27-9)

=-12.(3√3+3)/18

=-12.3(√3+1)/18

=-36(√3+1)/18 =-2(√3+1)

Answer 2

Resposta:

Explicação passo-a-passo:

$\dfrac{2}{(\sqrt{\frac{\sqrt{3}}{\sqrt{3}+3}})^{2}}=\dfrac{2}{{\frac{\sqrt{3}}{\sqrt{3}+3}}}=\\\\\\=\dfrac{2.(\sqrt{3}+3)}{\sqrt{3}}=\dfrac{2.(\sqrt{3}+\sqrt{3}.\sqrt{3})}{\sqrt{3}}=\dfrac{2.\sqrt{3}(1+\sqrt{3})}{\sqrt{3}}=2(1+\sqrt{3})$