Question

How to simplify `root(3)(24y^21x^5)` ?

Answer 1

`2xy^7root(3)(2x^2)`

Explanation:

Write the radicand as aproduct of prime factors.

`root(3) (24y^21x^5) =root(3) (3xx2^3y^21x^5)`

Write cubes where possible:
`root(3) (3xx2^3y^21x^5) = root(3) (3xxcolor(red)(2^3y^21x^3)xx x^2)`

Find the cube roots where possible by dividing the indices by `3`.

`=color(red)(2xy^7)root(3)(2x^2)`