I was wondering if there exists a reliable way to extract the $n$th root of a given number. For example, if you have a large perfect square such as 10,404, how would I go about taking its square root by hand?
And what about cube roots? Is there a way to find the cube root of any number by hand?
If there is a way to take the cube and square roots of any number, is there a technique that can be applied to extract the cube or square root of polynomials? What about any root?
I think that, if there is a way to take the $n$th root of any number of polynomial, I would benefit from learning it, since I consider being able to work with roots important to my algebra foundation.