What is the following quotient?

Choice C)

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Work Shown:

Part 1

Part 2

Part 3

This shows the answer is choice C.

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Explanation:

There are a lot of steps, so I broke things up into 3 sections or parts. The idea I'm applying is if the denominator is of the form , then multiplying top and bottom by will rationalize the denominator. This is due to the difference of squares rule (step 3 of part 1). The following step shows squaring a square root has the two cancel out.

From that point, I simplified each square root and factored to cancel out a pair of '4's.

To expand out , we can use either the FOIL method, the box method, or the distribution property. I used the distribution property.