## Example Questions

### Example Question #1 : How To Find The Common Factor Of Square Roots

Which of the following is equivalent to: ?      Explanation:

To begin with, factor out the contents of the radicals.  This will make answering much easier: They both have a common factor .  This means that you could rewrite your equation like this: This is the same as: These have a common .  Therefore, factor that out: ### Example Question #1 : How To Find The Common Factor Of Square Roots

Simplify:       Explanation:

These three roots all have a in common; therefore, you can rewrite them: Now, this could be rewritten: Now, note that Therefore, you can simplify again: Now, that looks messy! Still, if you look carefully, you see that all of your factors have ; therefore, factor that out: This is the same as: ### Example Question #1 : Factoring Common Factors Of Squares And Square Roots

Simplify the following:    It cannot be simplified any further  Explanation:

Begin by factoring each of the roots to see what can be taken out of each: These can be rewritten as: Notice that each of these has a common factor of .  Thus, we know that we can rewrite it as: ### Example Question #1 : How To Find The Common Factor Of Square Roots

Simplify the following:     The expression cannot be simplified any further. Explanation:

Clearly, all three of these roots have a common factor inside of their radicals. We can start here with our simplification. Therefore, rewrite the radicals like this: We can simplify this a bit further: From this, we can factor out the common : ### Example Question #611 : Gre Quantitative Reasoning       Explanation:

To attempt this problem, attempt to simplify the roots of the numerator and denominator: Notice how both numerator and denominator have a perfect square: The term can be eliminated from the numerator and denominator, leaving ### Example Question #1 : Factoring Common Factors Of Squares And Square Roots       Explanation:

For this problem, begin by simplifying the roots. As it stands, numerator and denominator have a common factor of in the radical: And as it stands, this is multiplied by a perfect square in the numerator and denominator: The term can be eliminated from the top and bottom, leaving ### Example Question #3 : How To Find The Common Factor Of Square Roots       Explanation:

To solve this problem, try simplifying the roots by factoring terms; it may be noticeable from observation that both numerator and denominator have a factor of in the radical: We can see that the denominator has a perfect square; now try factoring the in the numerator: We can see that there's a perfect square in the numerator: Since there is a in the radical in both the numerator and denominator, we can eliminate it, leaving ### All GRE Math Resources 