(3^{\frac{1}{4}}+5^{\frac{1}{4}})^2*(3^{\frac{1}{4}}-5^{\frac{1}{4}})^2=
(3^{\frac{1}{4}}+5^{\frac{1}{4}})(3^{\frac{1}{4}}+5^{\frac{1}{4}})*(3^{\frac{1}{4}}-5^{\frac{1}{4}})(3^{\frac{1}{4}}-5^{\frac{1}{4}})=
(\sqrt[4]3+\sqrt[4]5)(\sqrt[4]3+\sqrt[4]5)*(\sqrt[4]3-\sqrt[4]5)(\sqrt[4]3-\sqrt[4]5)=
(\sqrt[4]3+\sqrt[4]5)(\sqrt[4]3-\sqrt[4]5)*(\sqrt[4]3+\sqrt[4]5)(\sqrt[4]3-\sqrt[4]5)=
(a+b)(a-b)=a^2-b^2 wzór skróconego mnożenia
(\sqrt3-\sqrt5)*(\sqrt3-\sqrt5)=
(\sqrt3-\sqrt5)^2=3-2\sqrt{15}+5=8-2\sqrt{15}