ACT Math : Factoring Squares
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Example Questions
Example Question #1 : How To Factor A Common Factor Out Of Squares
Which real number satisfies 
Simplify the base of 9 and 27 in order to have a common base.
(3x)(9)=272
= (3x)(32)=(33)2
=(3x+2)=36
Therefore:
x+2=6
x=4
Example Question #2 : How To Factor A Common Factor Out Of Squares
Which of the following is a factor of 
The terms of 
Of the five choices, only 
Example Question #2 : How To Factor A Common Factor Out Of Squares
Simplify 
The easiest way to approach this problem is to break everything into exponents. 
Example Question #4 : Squaring / Square Roots / Radicals
Which of the following expression is equal to
When simplifying a square root, consider the factors of each of its component parts:
Combine like terms:
Remove the common factor, 
Pull the 
Example Question #5 : Squaring / Square Roots / Radicals
Which of the following is equal to the following expression?
First, break down the components of the square root:
Combine like terms. Remember, when multiplying exponents, add them together:
Factor out the common factor of 
Factor the 
Combine the factored 
Now, you can pull 
Example Question #6 : Squaring / Square Roots / Radicals
Which of the following expressions is equal to the following expression?
First, break down the component parts of the square root:
Combine like terms in a way that will let you pull some of them out from underneath the square root symbol:
Pull out the terms with even exponents and simplify:
Example Question #4 : How To Factor A Common Factor Out Of Squares
What is,
To find an equivalency we must rationalize the denominator.
To rationalize the denominator multiply the numerator and denominator by the denominator.
Factor out 6,
Extract perfect square 9 from the square root of 18.
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