Question

$\sqrt{ \sqrt{5} -1} * \sqrt[4]{6+2 \sqrt{5} }$

Answer 1

$\sqrt{ \sqrt{5}-1 } * \sqrt[4]{6+2 \sqrt{5} } =\sqrt{ \sqrt{5}-1 }*\sqrt[4]{(1+ \sqrt{5})^2 }=$$\sqrt{ \sqrt{5}-1 } * \sqrt{ \sqrt{5}+1 } = \sqrt{(\sqrt{5}-1)(\sqrt{5}+1 ) } = \sqrt{5-1} =2$