(\frac{1}{\sqrt5-\sqrt3})^3=(\frac{1*(\sqrt5+\sqrt3)}{(\sqrt5-\sqrt3)*(\sqrt5+\sqrt3)})^3=(\frac{\sqrt5+\sqrt3}{5-3})^3=(\frac{\sqrt5+\sqrt3}{2})^3=
{\frac{(\sqrt5)^3+3*(\sqrt5)^2*\sqrt3+3\sqrt5*(\sqrt3)^2+(\sqrt3)^3}{8}=\frac{3\sqrt5+3*5\sqrt3+3\sqrt5*3+3\sqrt3}{8}=}
{=\frac{3\sqrt5+15\sqrt3+9\sqrt5+3\sqrt3}{8}=\frac{18\sqrt3+14\sqrt5}{8}=\frac{\not2^1(9\sqrt3+7\sqrt5)}{\not8^4}=\frac{9\sqrt3+7\sqrt5}{4}}
wzór skróconego mnożenia:
(a+b)^3=a^3+3a^2b+3ab^2+b^3