Begin by multiplying what is under the square roots together. Remember:

Therefore:

We must now try to reduce the square root. Look for factors that can be taken out that can be easily square-rooted. It's a good idea to start with small square roots . In this case, we can factor out a 9 from 135:

Now take the square root of 9, and we are left with our answer:

To solve this problem, we must know how to multiply/divide with square roots. The rules involved are quite simple. When multiplying square roots together, multiply the coeffcients of the two numbers together and then multiply the two radicands together. The product of the radicand becomes the new radicand and the product of the coeffcients become the new coeffcient. The radicand is simply the number within the square root.

Dividing square roots follows the exact same rules as multiplying square roots, divide the coeffcients together, the result is the coeffcient for final answer. Do the same for the radicands.

Begin by breaking down each of the roots in question.  Often, for the GRE, your answer arises out of doing such basic "simplification moves".

Quantity A

This is the same as:

, which can be reduced to:

Quantity B

This is the same as:

, which can be reduced to:

Now, since we know that  must be greater than , we know that .  Therefore, quantity A is larger.

Begin by subtracting  from both sides:

This simplifies to:

Now, while you could square both sides, you also know that  merely needs to be the same as the value under the other radical. This means that it is —simply and quickly! (Always work to save time on the exam!)

As always for comparison questions, work on getting your quantities explicit. In order to do this in this case, you must factor the roots.

Quantity A

This can be factored into:

Quantity B

This can be factored into:

This makes the comparison very easy! Since  is a larger number than , we know that  is a smaller value than . Therefore, Quantity B is larger.

At first, this problem seems rather easy. You merely need to divide these two values to get:

However, there are no answers that look like this! When this happens, you should consider rationalizing the denominator to eliminate the square root. This is a little more difficult than normal problems like this (ones that contain only the radical). However, if you complete a difference of squares in the denominator, you will be well on your way to having the right answer:

Carefully FOIL your denominator and distribute your numerator:

Look to your answers for an idea for factoring your numerator:

Note that 

This changes the initial equation to

For this equation to be valid, the exponents must be equal:

In order to solve for , the equation  must be written such that each set of exponents shares the same base:

Which like bases, it's now just a matter of solving for :

To find an equivalent, just multiply the top and bottom by the conjugate of the denominator.

Conjugate is the square root expression found in the denominator but with opposite sign.

So:

By simplifying, we get .

Since in all the answer choices have an integer in the denominator, we should multiply top and bottom by the conjugate of the denominator which is the square root expression with opposite sign.

So:

If we redistribute the negative, then the answer becomes 

.