GRE Math : How to find the common factor of square roots
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Example Questions
Example Question #1 : Basic Squaring / Square Roots
Which of the following is equivalent to:
To begin with, factor out the contents of the radicals. This will make answering much easier:
They both have a common factor 
This is the same as:
These have a common 
Example Question #25 : Arithmetic
Simplify:
These three roots all have a 
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 
This is the same as:
Example Question #31 : Arithmetic
Simplify the following:
It cannot be simplified any further
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 
Example Question #32 : Basic Squaring / Square Roots
Simplify the following:
The expression cannot be simplified any further.
Clearly, all three of these roots have a common factor 
We can simplify this a bit further:
From this, we can factor out the common 
Example Question #5 : How To Find The Common Factor Of Square Roots
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 
Example Question #32 : Arithmetic
For this problem, begin by simplifying the roots. As it stands, numerator and denominator have a common factor of 
And as it stands, this 
The 
Example Question #612 : Gre Quantitative Reasoning
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 
We can see that the denominator has a perfect square; now try factoring the 
We can see that there's a perfect square in the numerator:
Since there is a 
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