Question

$\sqrt[4]{3+\sqrt{5} } *\sqrt[4]{3-\sqrt{5} }$

Answer 1

$\sqrt[4]{3+\sqrt{5} } * \sqrt[4]{3-\sqrt{5} } = \sqrt[4]{(3+\sqrt{5})(3-\sqrt{5} ) } =\sqrt[4]{3^{2}-\sqrt{5}^{2}   } =\sqrt[4]{9-5} =\sqrt[4]{4} =\sqrt[4]{2^{2} } =\sqrt{2}$