Dividing radical expressions with variables

Ok i understandhow to minimize something like this Sqroot of 720...for example but what if there was a variable how do i break it up along with the 720?
For example Sqroot720x^9
and then what if it was in a fraction
Example Sqroot720^9 how would i break up the denominator?
-----------------
y^9

You simplify square roots by looking for factors that are perfect squares.

x^9 has a factor x^8 which is a perfect square, so sqrt(x^9) = sqrt(x*x^8) = sqrt(x) * x^4.

sqrt(720^9/y^9) = sqrt(720^9) / sqrt(y^9) = 720^4 sqrt(720) / [y^4 sqrt(y)]

and you can further simplify sqrt(720) by pulling out factors that are squares.

If the square root is only on the top of the fraction:

sqroot 720^9
720^4 sqroot 720
just breakup the numerator and put it on top of y^9
and thats your answer
you cannot simpilfy it any further unless the bases were the same or had a common multiple

If the square root is on the top and bootom of the fraction:

720^4 sqrt 720
---------------------
y^4 sqrt y

Your Welcome!

I think you still made a mistake about your expression, so i'll address the exponent with variable problem

when it comes to variables, it's just basic division; the square root is represented by a '2'...

√y^9 = y^(9/2)

so how can we separate it? the same way with numbers, through multiplication.

√(y^9) = √(y^8 times y^1)

√y^8 times √y

y^(8/2) times √y

y^4 times √y

y^4√y