### All GRE Math Resources

## Example Questions

### Example Question #21 : Arithmetic

Which of the following is equivalent to:

?

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

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 #3 : Factoring Common Factors Of Squares And Square Roots

Simplify the following:

**Possible Answers:**

It cannot be simplified any further

**Correct answer:**

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 #4 : Factoring Common Factors Of Squares And Square Roots

Simplify the following:

**Possible Answers:**

The expression cannot be simplified any further.

**Correct answer:**

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 #31 : Arithmetic

**Possible Answers:**

**Correct answer:**

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

**Possible Answers:**

**Correct answer:**

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 #1 : Factoring Common Factors Of Squares And Square Roots

**Possible Answers:**

**Correct answer:**

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