Doubling the cube cube involve neusis, the cissoid of Diocles, the conchoid of Nicomedes, or the Philo line. Archytas solved the problem in the 4th century BC using geometric construction in three dimensions, determining a certain point as the intersection of three surfaces of revolution. False claims of doubling the cube with compass and straightedge abound in mathematical crank literature (pseudomathematics). Origami may also be used to construct the cube root of two by folding paper. There is a simple neusis construction using a marked ruler for a length which is the cube root of 2 times another length. Then AG is the
Nth root real. Finally, if "x" is not real, then none of its "n"th roots is real. Roots are usually written using the radical symbol or "radix" with formula_2 denoting the principal square root of formula_3, formula_4 denoting the principal cube root, formula_5 denoting the principal fourth root, and so on. In the expression formula_6, "n" is called the "index", formula_7 is the "radical sign" or "radix", and formula_3 is called the "radicand". Since the radical symbol denotes a function, it is defined to return only one result for a given argument formula_3, which is called the principal "n"th root of formula_3.