GRE Math : How to subtract square roots
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Example Questions
Example Question #21 : Square Roots And Operations
Quantity A:
Quantity B:
Which of the following is true?
The relationship cannot be determined from the information provided.
Quantity A is larger.
Quantity B is larger.
The two quantities are equal.
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 
Example Question #57 : Arithmetic
Solve for 
Note, 
Begin by subtracting 
This simplifies to:
Now, while you could square both sides, you also know that 
Example Question #21 : Square Roots And Operations
Quantity A:
Quantity B:
Which of the following is true?
The relationship cannot be determined from the information provided.
The two quantities are equal.
Quantity B is larger.
Quantity A is larger.
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 
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