I really don't know why you call this problem a "Quickie" (I still have a crack in my head!)
It took some time until I remembered the property:
If x > y > 0 then
With these properties your term becomes:
Expand the brackets and collect the roots with the same value. I've got:
Lovely work, Galactus and EB!
Don't know if the "Quickie" solution is any faster . . .
We have: .
Multiply top and bottom by