Question

suppose you know that \[\sqrt[n]{a/b}\] is a rational number and that "a" and "b" have no common factors. What can you say about the prime factorizations of "a" and "b"?

Answer 1

must be perfect squares

Answer 2

but n could be something else
sqrt[n]{a/b} = \[\sqrt[n]{a/b}\]

Answer 3

then replace "square" by \(nth\)

Answer 4

ok, thanks