All ACT Math Resources
Example Question #1 : Factoring Squares
Which real number satisfies ?
Simplify the base of 9 and 27 in order to have a common base.
Example Question #122 : Exponents
Which of the following is a factor of ?
The terms of have as their greatest common factor, so
is a prime polynomial.
Of the five choices, only is a factor.
Example Question #1 : How To Factor A Common Factor Out Of Squares
The easiest way to approach this problem is to break everything into exponents. is equal to and 27 is equal to . Therefore, the expression can be broken down into . When you cancel out all the terms, you get , which equals .
Example Question #4 : Factoring Squares
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 outside of the equation as :
Example Question #2 : How To Factor A Common Factor Out Of Squares
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 with the :
Now, you can pull out from underneath the square root sign as :
Example Question #4 : 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
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.