All GRE Math Resources
Example Questions
Example Question #4 :How To Simplify Square Roots
Simplify.
Example Question #5 :How To Simplify Square Roots
Simplfy the following radical.
You can rewrite the equation as.
This simplifies to.
Example Question #1 :How To Simplify Square Roots
Which of the following is equal to?
√75 can be broken down to √25 * √3. Which simplifies to 5√3.
Example Question #2 :Exponents And Roots
Simplify.
Rewrite what is under the radical in terms of perfect squares:
Therefore,.
Example Question #1 :Simplifying Square Roots
What is?
We know that 25 is a factor of 50. The square root of 25 is 5. That leaveswhich can not be simplified further.
Example Question #4 :Exponents And Roots
Which of the following is equivalent to?
Multiply by the conjugate and the use the formula for the difference of two squares:
Example Question #5 :Exponents And Roots
Which of the following is the most simplified form of:
First find all of the prime factors of
So
Example Question #6 :Exponents And Roots
What isequal to?
1. We know that, which we can separate under the square root:
2. 144 can be taken out since it is a perfect square:. This leaves us with:
This cannot be simplified any further.
Example Question #1 :Factoring Common Factors Of Squares And 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 means that you could rewrite your equation like this:
This is the same as:
These have a common. Therefore, factor that out:
Example Question #2 :Factoring Common Factors Of Squares And Square Roots
Simplify:
These three roots all have ain 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: