# What is the simplest form of the expression ?  `(sqrt(6x^8y^9))/(sqrt(5x^2y^4))`

`(sqrt(6x^8y^9))/(sqrt(5x^2y^4))`

Combine the radical expressions into one single expression.

`sqrt((6x^8y^9)/(5x^2y^4))`

Remove the common factor of `x^2y^4` from both the numerator and denominator.

`sqrt((6x^6y^5)/(5))`

Pull out the perfect square roots from beneath the radical. `x^3y^2` is a perfect square.

`x^3y^2 * sqrt((6y)/(5))`

Now split the fraction under the radical into...

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`(sqrt(6x^8y^9))/(sqrt(5x^2y^4))`

Combine the radical expressions into one single expression.

`sqrt((6x^8y^9)/(5x^2y^4))`

Remove the common factor of `x^2y^4` from both the numerator and denominator.

`sqrt((6x^6y^5)/(5))`

Pull out the perfect square roots from beneath the radical. `x^3y^2` is a perfect square.

`x^3y^2 * sqrt((6y)/(5))`

`x^3y^2 *sqrt(6y)/(sqrt5)`

In order to rationalize the denominator, the fraction must be rewritten. The factor to multiply by must be an expression that will remove the radical from the denominator.

`x^3y^2* (sqrt(6y)/sqrt5) * ((sqrt5)/(sqrt5))`

Multiply `sqrt5 by sqrt5` to get 5.

This leaves

`x^3y^2 *((sqrt5sqrt(6y))/(5))`

Simplify the rationalized expression.

The solution is:

`x^3y^2sqrt(30y)/5`

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