For slightly greater clarity, write this expression as
sqrt(6x^8y^9) 6x^8y^9
-------------------- This is equivalent to sqrt[ -------------------- ]
sqrt(5x^2y^4) 5x^2y^4
Reduce the quantity inside the square brackets, obtaining:
6*x^6*y^5
sqrt[ ---------------- ]
5
This simplifies as follows: sqrt[ 6/5 ] * [ x^3 * y^(5/2)
which can be simplified even further if you wish.
