How to find a ratio of square roots - GRE Quantitative Reasoning
Card 0 of 6
Which of the following is equivalent to the ratio of 
to 
?
Which of the following is equivalent to the ratio of
At first, this problem seems rather easy. You merely need to divide these two values to get:
However, there are no answers that look like this! When this happens, you should consider rationalizing the denominator to eliminate the square root. This is a little more difficult than normal problems like this (ones that contain only the radical). However, if you complete a difference of squares in the denominator, you will be well on your way to having the right answer:
Carefully FOIL your denominator and distribute your numerator:
Look to your answers for an idea for factoring your numerator:
At first, this problem seems rather easy. You merely need to divide these two values to get:
However, there are no answers that look like this! When this happens, you should consider rationalizing the denominator to eliminate the square root. This is a little more difficult than normal problems like this (ones that contain only the radical). However, if you complete a difference of squares in the denominator, you will be well on your way to having the right answer:
Carefully FOIL your denominator and distribute your numerator:
Look to your answers for an idea for factoring your numerator:
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Which of the following is equal to 
?
Which of the following is equal to
To find an equivalent, just multiply the top and bottom by the conjugate of the denominator.
Conjugate is the square root expression found in the denominator but with opposite sign.
So:
By simplifying, we get 
.
To find an equivalent, just multiply the top and bottom by the conjugate of the denominator.
Conjugate is the square root expression found in the denominator but with opposite sign.
So:
By simplifying, we get
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Which of the following has the same ratio as 
?
Which of the following has the same ratio as
Since in all the answer choices have an integer in the denominator, we should multiply top and bottom by the conjugate of the denominator which is the square root expression with opposite sign.
So:
If we redistribute the negative, then the answer becomes
.
Since in all the answer choices have an integer in the denominator, we should multiply top and bottom by the conjugate of the denominator which is the square root expression with opposite sign.
So:
If we redistribute the negative, then the answer becomes
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What is the ratio of 
expressed in 
form?
What is the ratio of
To get into 
form, multiply the fraction by bottom denominator's reciprocal.
The 
is the numerator of the fraction and 
is the denominator.
Final answer is 
.
To get into
The
Final answer is
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What is 
if 
?
What is
Note that 
This changes the initial equation to
For this equation to be valid, the exponents must be equal:
Note that
This changes the initial equation to
For this equation to be valid, the exponents must be equal:
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Given the equation 
, solve for 
.
Given the equation
In order to solve for 
, the equation 
must be written such that each set of exponents shares the same base:
Which like bases, it's now just a matter of solving for 
:
In order to solve for
Which like bases, it's now just a matter of solving for
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