Hensel's lemma the value of "c" mod 27: if "c" ≡ 1 mod 27 then use "a" = 1, if "c" ≡ 10 mod 27 then use "a" = 4 (since 4 is a root of "f"("x") mod 27), and if "c" ≡ 19 mod 27 then use "a" = 7. (It is not true that every "c" ≡ 1 mod 3 is a 3-adic cube, e.g., 4 is not a 3-adic cube since it is not a cube mod 9.) In a similar way, after some preliminary work Hensel's lemma can be used to show that for any "odd" prime number
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.