What is the simplest form of the expression ?


Expert Answers

An illustration of the letter 'A' in a speech bubbles


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:


See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial