How to find the common factor of square roots - GRE Quantitative Reasoning
Card 1 of 56
Which of the following is equivalent to:
?
Which of the following is equivalent to:
Tap to reveal 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:
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
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Simplify:
Simplify:
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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:
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:
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Simplify the following:
Simplify the following:
Tap to reveal 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:
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
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Simplify the following:
Simplify the following:
Tap to reveal 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 
:
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
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Tap to reveal 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
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
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Tap to reveal 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
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
← Didn't Know|Knew It →
Tap to reveal 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
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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Which of the following is equivalent to:
?
Which of the following is equivalent to:
Tap to reveal 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:
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
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Simplify:
Simplify:
Tap to reveal 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:
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:
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Simplify the following:
Simplify the following:
Tap to reveal 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:
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
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Simplify the following:
Simplify the following:
Tap to reveal 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 :
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
← Didn't Know|Knew It →
Tap to reveal 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
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
← Didn't Know|Knew It →
Tap to reveal 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
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
← Didn't Know|Knew It →
Tap to reveal 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
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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Which of the following is equivalent to:
?
Which of the following is equivalent to:
Tap to reveal 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:
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
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Simplify:
Simplify:
Tap to reveal 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:
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:
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Simplify the following:
Simplify the following:
Tap to reveal 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:
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
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Simplify the following:
Simplify the following:
Tap to reveal 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 :
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
← Didn't Know|Knew It →
Tap to reveal 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
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
← Didn't Know|Knew It →
Tap to reveal 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
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
← Didn't Know|Knew It →