Question

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

Answer 1

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