Question

How do divide radical expressions?

Answer 1

If the radicals are of the same power, then they can be combined under a common radical sign
`(root(a)(p)) / (root(a)(q)) = root(a)(p/q)`

e.q.
`(root(2)(27))/(root(2)(75)) = root(2)(27/75) = root(2)(((3)(9))/((3)(25))) = 3/4`

If the radicals are of different powers:
`(root(a)(p)) = (root(b)(q))`

`rarr (root(a*b)(p^b))/(root(a*b)(q^a))`

`rarr root(a*b)(p^b/q^a)`