How do you divide #sqrt(12x^3y^12)/sqrt(27xy^2)#?
Take one big root to get:
and finally taking the square root:
Hope it helps!
There are several good approaches to this question:
The reason I try this is that I see some common factors. Namely
Write it as a single square root, then simplify, the break it up into smaller square roots.
Or simplify both numerator and denominator, then simplify what you can.
(Rationalizing the denominator would work too, eventually.)