math
posted by Jane on .
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

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! 
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! 
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