How do I quickly calculate cube roots? (Lord it's been forever since I last been on here.)

Using a calculator is the quickest method.

Memorizing or just knowing what the first few are.

Then there's prime factorization method. Prime factor and then find 3 groups.

Example:

Square root of 1,728

864 * 2

432 * 2 * 2

216 * 2 * 2 * 2

108 * 2 * 2 * 2 * 2

54 * 2 * 2 * 2 * 2 * 2

27 * 2 * 2 * 2 * 2 * 2 * 2

9 * 3 * 2 * 2 * 2 * 2 * 2 * 2

3 * 3 * 3 * 2 * 2 * 2 * 2 * 2 * 2

Make 3 groups of the same of primes ...

(3 * 2 * 2) * (3 * 2 * 2) * (3 * 2 * 2)

12 * 12 * 12 = 1,728

12³ = 1,728