GRE Math : How to subtract square roots

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1 : How To Subtract Square Roots

Quantity A: 

Quantity B: 

Which of the following is true?

Possible Answers:

The two quantities are equal.

Quantity B is larger.

The relationship cannot be determined from the information provided.

Quantity A is larger.

Correct answer:

Quantity A is larger.

Explanation:

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.

Example Question #2 : How To Subtract Square Roots

Solve for .

Note, :

Possible Answers:

Correct answer:

Explanation:

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!)

Example Question #3 : How To Subtract Square Roots

Quantity A: 

Quantity B:

Which of the following is true?

Possible Answers:

The relationship cannot be determined from the information provided.

The two quantities are equal.

Quantity A is larger.

Quantity B is larger.

Correct answer:

Quantity B is larger.

Explanation:

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.

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