Simplify the radical expression by rationalizing the denominator:

2(square root)108 / (square root) 180y

Please show me how to set up and how to solve

Oops! Forgot to carry the y along in both the numerator and denominator.

From this point on, here's how it works out:

Try to find factors to reduce this radical expression:

2√(2*2*3*3*3) * √(2*2*3*3*5*y)
----------------------------
180y

Now we have:

2*2*3*√3 * 2*3*√5y
-----------------
180y

12√3 * 6√5y
----------
180y

72√15y
------
180y

Reduces to:

2√15y
----
5y

Sorry for any confusion!

I'm going to assume your problem is this:

2√108
-----
√180y

Multiply both the top and bottom by the equivalent of 1.

2√108.....√180y
----- X -------
√180y.....√180y

Now we have:

2√108 * √180y
-------------
180y

Try to find factors to reduce this radical expression:

2√(2*2*3*3*3) * √(2*2*3*3*5)
----------------------------
180y

Now we have:

2*2*3*√3 * 2*3*√5
-----------------
180y

12√3 * 6√5
----------
180y

72√15
------
180y

Reduces to:

2√15
----
5

And there you have it!

THANK YOU MY GOD YOU SAVED MY LIFE

Thank you for your help, MathGuru.

Thanks

To simplify the given radical expression by rationalizing the denominator, the key is to remove any radical expressions from the denominator. Follow these steps:

Step 1: Identify the highest perfect square factor that can be extracted from both the numerator and the denominator. In this case, find the highest perfect square factor that can be extracted from 108, 180, and y.

Step 2: Simplify the numerator. To simplify the square root of 108, break it down into its prime factors: 108 = 2^2 * 3^3. Since we want to extract the highest perfect square, we can rewrite the square root of 108 as 6 * sqrt(3).

Step 3: Simplify the denominator. Similarly, for the square root of 180, break it down into its prime factors: 180 = 2^2 * 3^2 * 5. Again, we want to extract the highest perfect square, so we can rewrite the square root of 180 as 6 * sqrt(5).

Now, let's rewrite the given expression with the simplified numerator and denominator:

2 * sqrt(108) / sqrt(180y)

= 2 * (6 * sqrt(3)) / (6 * sqrt(5) * sqrt(y))

= 12 * sqrt(3) / (6 * sqrt(5) * sqrt(y))

= 2 * sqrt(3) / (sqrt(5) * sqrt(y))

We have successfully rationalized the denominator by eliminating the radical in the denominator. The simplified expression is 2 * sqrt(3) / (sqrt(5) * sqrt(y)).