Casus irredicibilis describes a situation where a cubic polynomial with integer coefficients has three distinct real roots, but you can't express those roots using just real numbers and radicals. Instead, if you want to only use radicals, then you must use complex numbers, even though the roots you're interested are purely real. The example that Planet Math gives is x^3 - 3x +1, but one of the roots of this cubic is negative. This is unsatisfying for me, because in the 1500's when Cardano first discovered the phenomena that cubic equations could not be solved with real numbers alone, the existence of negative numbers had not yet been commonly accepted. So in order to be more historically "authentic", I would prefer an example of casus irreducibilis where all three roots are positive. Does anyone know of such an example? Any help would be greatly appreciated. Thank You in Advance.