GRE Math : How to divide square roots

Study concepts, example questions & explanations for GRE Math

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Example Questions

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Example Question #631 : Gre Quantitative Reasoning

Solve for :

Possible Answers:

Correct answer:

Explanation:

To get rid of the radical, multiply top and bottom by .

 

Square both sides.

Example Question #52 : Basic Squaring / Square Roots

Simplify:

Possible Answers:

Correct answer:

Explanation:

 is "opposite over adjacent," or . (This is because .)

Let's substitute  into the equation for  and multiply the numerator and the denominator by .

Now we can multiply the result by 

 is the inverse of , or :

We can reduce the resulting  to 

 

By multiplying top and bottom by , we can cancel out the  in the numerator:

The resulting fraction can be simplified:

Example Question #11 : How To Divide Square Roots

Simplify.

Possible Answers:

Correct answer:

Explanation:

To get rid of the radical, we need to multiply by the conjugate. The conjugate uses the opposite sign and multiplying by it will let us rationalize the denominator in this problem. The goal is getting an expression of  in which we are taking the differences of two squares.

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