Can you express n-th degree roots as n-th roots and n-sections?

I have zero, one, addition, subtraction, multiplication, division (by a non-zero expressible number), n-th roots (of positive expressible numbers, where n is expressible), and all the trigonometric functions (in their default domain restricted to the expressible numbers). The number expressible with these operations are called expressible.

Can this allow me to construct n-th degree roots, i.e. a root of an arbitrary n-th degree polynomial, presuming it has a real root?