How to subtract square roots - GRE Quantitative Reasoning
Card 0 of 3
Quantity A: 
Quantity B: 
Which of the following is true?
Quantity A:
Quantity B:
Which of the following is true?
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 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:
Quantity B
This is the same as:
Now, since we know that
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Solve for 
.
Note, 
:
Solve for
Note,
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!)
Begin by subtracting
This simplifies to:
Now, while you could square both sides, you also know that
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Quantity A: 
Quantity B:
Which of the following is true?
Quantity A:
Quantity B:
Which of the following is true?
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.
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
Compare your answer with the correct one above