Question

IFPI-2018.1
45. O produto $\sqrt{3 + \sqrt{5}}$ · $\sqrt{3 - \sqrt{5}}$ é igual a:
a) $\sqrt{2}$
b) $\sqrt{3}$
c) 2
d) 3
e) $\sqrt{5}$

Answer 1

$\sqrt{3+\sqrt{5}}~.~\sqrt{3-\sqrt{5}}~=\\\\\\=~\sqrt{\left(3+\sqrt{5}\right)~.~\left(3-\sqrt{5}\right)}\\\\\\=~\sqrt{3~.~3~-~3~.~\sqrt{5}~+~\sqrt{5}~.~3~-~\sqrt{5}~.~\sqrt{5}}\\\\\\=~\sqrt{9~-~3\sqrt{5}~+~3\sqrt{5}~-~\sqrt{5}^{\,2}}\\\\\\=~\sqrt{9~+~0~-~5}\\\\\\=~\sqrt{4}\\\\\\=~\boxed{2}$

Resposta: Letra C