Factoring Squares - ACT Math
Card 0 of 63
Which real number satisfies
?
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
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
Compare your answer with the correct one above
Which of the following is a factor of
?
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.
The terms of have
as their greatest common factor, so
is a prime polynomial.
Of the five choices, only is a factor.
Compare your answer with the correct one above
Which of the following expressions is equal to the following expression?

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:

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:
Compare your answer with the correct one above
Which of the following is equal to the following expression?

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
:

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
:
Compare your answer with the correct one above
Which of the following expression is equal to

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
:

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
:
Compare your answer with the correct one above
Simplify 
Simplify
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
.
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
.
Compare your answer with the correct one above
What is,
?
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.



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.
Compare your answer with the correct one above
Which real number satisfies
?
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
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
Compare your answer with the correct one above
Which of the following is a factor of
?
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.
The terms of have
as their greatest common factor, so
is a prime polynomial.
Of the five choices, only is a factor.
Compare your answer with the correct one above
Which of the following expressions is equal to the following expression?

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:

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:
Compare your answer with the correct one above
Which of the following is equal to the following expression?

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
:

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
:
Compare your answer with the correct one above
Which of the following expression is equal to

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
:

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
:
Compare your answer with the correct one above
Simplify 
Simplify
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
.
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
.
Compare your answer with the correct one above
What is,
?
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.



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.
Compare your answer with the correct one above
Which real number satisfies
?
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
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
Compare your answer with the correct one above
Which of the following is a factor of
?
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.
The terms of have
as their greatest common factor, so
is a prime polynomial.
Of the five choices, only is a factor.
Compare your answer with the correct one above
Which of the following expressions is equal to the following expression?

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:

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:
Compare your answer with the correct one above
Which of the following is equal to the following expression?

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
:

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
:
Compare your answer with the correct one above
Which of the following expression is equal to

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
:

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
:
Compare your answer with the correct one above
Simplify 
Simplify
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
.
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
.
Compare your answer with the correct one above