All SAT Math Resources
Example Questions
Example Question #1 :Factoring And Simplifying Square Roots
Solve for:
Notice how all of the quantities in square roots are divisible by 9
Simplifying, this becomes
Example Question #1 :How To Find The Common Factor Of Square Roots
Solve for:
Note that all of the square root terms share a common factor of 36, which itself is a square of 6:
Factoringfrom both terms on the left side of the equation:
Example Question #2 :Basic Squaring / Square Roots
Solve for:
Note that bothandhave a common factor ofandis a perfect square:
From here, we can factorout of both terms on the lefthand side
Example Question #3 :Basic Squaring / Square Roots
Solve for:
In order to solve for, first note that all of the square root terms on the left side of the equation have a common factor of 9 and 9 is a perfect square:
Simplifying, this becomes:
Example Question #2 :How To Find The Common Factor Of 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 #1 :How To Find The Common Factor Of 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:
Example Question #4 :Basic Squaring / Square Roots
Solve for:
Examining the terms underneath the radicals, we find thatandhave a common factor of.itself is a perfect square, being the product ofand. Hence, we recognize that the radicals can be re-written in the following manner:
, and.
The equation can then be expressed in terms of these factored radicals as shown:
Factoring the common termfrom the lefthand side of this equation yields
Divide both sides by the expression in the parentheses:
Divide both sides byto yieldby itself on the lefthand side:
Simplify the fraction on the righthand side by dividing the numerator and denominator by:
This is the solution for the unknown variablethat we have been required to find.
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