Is the Square root of 7 divided by cube root of 15 irrational?

Answer 1

0.4667

Answer 2

Probably. Calculations of two Irrational Numbers will almost always result in another irrational number, unless the "irrationality" somehow gets cancelled by carefully choosing your numbers, for example, (10 - root(2)) + root(2), or root(3) / root(3).

Proving irrationality in specific cases may be more difficult, though.