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 group: Find the square root of 152.2756. Find the cube root of 4192 to the nearest hundredth. The principal "n"th root of a positive number can be computed using logarithms. Starting from the equation that defines "r" as an "n"th root of "x", namely formula_80 with "x" positive and therefore its principal root "r" also positive, one takes logarithms of both sides (any base of the logarithm will do) to obtain The root "r" is recovered from this by taking the antilog: For the case in which "x" is negative and "n" is odd, there is one real root "r"