Homework Help

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

connorcolin3's profile pic

Posted via web

dislike 2 like

What is the simplest form of the expression ?


1 Answer | Add Yours

jgeertz's profile pic

Posted (Answer #1)

dislike 1 like



Combine the radical expressions into one single expression.


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


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 separate radical expressions.

`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:




Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes