Question

Simplificando a expressão E = −√ + √, encontramos como resultado para E:
a) – 3
b) 3
c) 2
d) √3
e) 1 - √3

Answer 1

$\boxed{\boxed{a) \ -3}}\\\\\\E = \dfrac{6}{1-\sqrt{3}} + \sqrt{27}\\\\E = \dfrac{6}{1-\sqrt{3}} \cdot \dfrac{1+\sqrt{3}}{1+\sqrt{3}} + 3\sqrt{3}\\\\E = \dfrac{6 + 6\sqrt{3}}{1^2-\sqrt{3}^2} + 3\sqrt{3}\\\\E = \dfrac{6 + 6\sqrt{3}}{1-3} + 3\sqrt{3}\\\\E = -\dfrac{6 + 6\sqrt{3}}{2} + 3\sqrt{3}\\\\E = -3 -3\sqrt{3}+3\sqrt{3}\\\\E = -3$