Question

(
$( \sqrt{ 3 + \sqrt{5} } - \sqrt{3 - \sqrt{5} }) { }^{2}$
​

Answer 1

$\sf \left(\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}\right)^2\\\\\\{Aplique\:a\:formula\:do\:quadrado\:perfeito}:\quad \left(a-b\right)^2=a^2-2ab+b^2\\\\\\a=\sqrt{3+\sqrt{5}},\:\:b=\sqrt{3-\sqrt{5}}\\\\\\=\left(\sqrt{3+\sqrt{5}}\right)^2-2\sqrt{3+\sqrt{5}}\sqrt{3-\sqrt{5}}+\left(\sqrt{3-\sqrt{5}}\right)^2\\\\\\\to \boxed{\sf \red{=2}}$