Question

How do you divide `sqrt(12x^3y^12)/sqrt(27xy^2)`?

Answer 1

Take one big root to get:

and finally taking the square root:
`=2/3*xy^5`

Hope it helps!

Answer 2

There are several good approaches to this question:
The reason I try this is that I see some common factors. Namely `3`, `x`, and `y^2`

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.

`sqrt(12x^3y^12)/sqrt(27xy^2)=sqrt((12x^3y^12)/(27xy^2))=sqrt((4x^2y^10)/9)=(2xy^5)/3`

Or:

`sqrt(12x^3y^12)/sqrt(27xy^2)=(sqrt(4*3*x^2*x*y^12))/(sqrt(9*3*x*y^2))=(2xy^6sqrt(3x))/(3ysqrt(3x))=(2xy^5)/3`

(Rationalizing the denominator would work too, eventually.)