# math

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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

• math -

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!

• Correction -

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!

• math -

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