Question

What is the simplest form of the expression? sqr root 6x^8y^9/ sqr root 5x^2y^4

Answer 1

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.