Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : How to factor a common factor out of squares

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Factor A Common Factor Out Of Squares

Which real number satisfies $3^{x}*9=27^{2}$ ?

Possible Answers:

Correct answer:

Explanation:

Simplify the base of 9 and 27 in order to have a common base.

(3^x)(9)=27²

= (3^x)(3²)=(3³)²

=(3^x+2)=3⁶

Therefore:

x+2=6

x=4

Report an Error

Example Question #2 : How To Factor A Common Factor Out Of Squares

Which of the following is a factor of $4x^{4}+ 36 x^{2}$ ?

Possible Answers:

$x^{2}+ 3$

$x^{2}+ 9$

$2x^{2}+ 9$

$x^{2}+ 6$

$2x^{2}+ 3$

Correct answer:

$x^{2}+ 9$

Explanation:

The terms of $4x^{4}+ 36 x^{2}$ have $4x^{2}$ as their greatest common factor, so

$4x^{4}+ 36 x^{2} = 4x^{2} (x^{2}+9)$

$x^{2}+ 9$ is a prime polynomial.

Of the five choices, only $x^{2}+ 9$ is a factor.

Report an Error

Example Question #1 : Factoring Squares

Simplify $\frac{8^{3} \times 3}{2^{6}\times 27}$

Possible Answers:

$\frac{16}{9}$

$\frac{9}{8}$

$\frac{32}{9}$

$\frac{8}{9}$

$\frac{4}{3}$

Correct answer:

$\frac{8}{9}$

Explanation:

The easiest way to approach this problem is to break everything into exponents. $8^{3}$ is equal to $2^{9}$ and 27 is equal to $3^{3}$ . Therefore, the expression can be broken down into $\frac{2^{9} \times 3}{2^{6}\times 3^{3}}$ . When you cancel out all the terms, you get $\frac{2^{3}}{3^{2}}$ , which equals $\frac{8}{9}$ .

Report an Error

Example Question #1 : How To Factor A Common Factor Out Of Squares

Which of the following expression is equal to

$\sqrt{(45)(9)+(27)(36)}$

Possible Answers:

$7\sqrt{15}$

$9\sqrt{17}$

$9\sqrt{15}$

$9\sqrt{19}$

$7\sqrt{17}$

Correct answer:

$9\sqrt{17}$

Explanation:

$\sqrt{(45)(9)+(27)(36)}$

When simplifying a square root, consider the factors of each of its component parts:

$\sqrt{(3^2)\times5\times(3^{2})+(3^{3})(2^2)(3^2)}$

Combine like terms:

$\sqrt{5(3^4)+(2^2)(3^5)}$

Remove the common factor, 3^4 :

$\sqrt{(3^4)\times(5+3\times(2^2))}$

Pull the $\sqrt{3^4}$ outside of the equation as 3^2 :

$(3^2)\sqrt{5+12}=9\sqrt{17}$

Report an Error

Example Question #5 : How To Factor A Common Factor Out Of Squares

Which of the following is equal to the following expression?

$\sqrt{(16)(8)+(32)(20)}$

Possible Answers:

$2^{3}\sqrt{6}$

$2^{7}\sqrt{5}$

$2^{3}\sqrt{10}$

$2^4\sqrt{3}$

$2^{4}\sqrt{5}$

Correct answer:

$2^4\sqrt{3}$

Explanation:

$\sqrt{(16)(8)+(32)(20)}$

First, break down the components of the square root:

$\sqrt{(2^{4})(2^{3})+(2^{5})(2^{2})\times 5}$

Combine like terms. Remember, when multiplying exponents, add them together:

$\sqrt{(2^{7})+(2^{7})\times5}$

Factor out the common factor of 2^7 :

$\sqrt{(2^{7})(1+5)}$

$\sqrt{(2^7)\times6}$

Factor the :

$\sqrt{(2^7)\times2\times3}$

Combine the factored with the 2^7 :

$\sqrt{(2^{8})\times3}$

Now, you can pull $\sqrt{2^8}$ out from underneath the square root sign as 2^4 :

$2^4\sqrt{3}$

Report an Error

Example Question #6 : How To Factor A Common Factor Out Of Squares

Which of the following expressions is equal to the following expression?

$\sqrt{(27)(45)(125)}$

Possible Answers:

$225\sqrt{3}$

$125\sqrt{27}$

$135\sqrt{5}$

$205\sqrt{3}$

$75\sqrt{20}$

Correct answer:

$225\sqrt{3}$

Explanation:

$\sqrt{(27)(45)(125)}$

First, break down the component parts of the square root:

$\sqrt{(3^{3})(5\times 3^{2})(5^{3})}$

Combine like terms in a way that will let you pull some of them out from underneath the square root symbol:

$\sqrt{(5^{4})(3^4)(3)}$

Pull out the terms with even exponents and simplify:

$(5^{2})(3^{2})\sqrt{3}=225\sqrt{3}$

Report an Error

Example Question #2321 : Act Math

What is,

$\frac{12}{\sqrt{18}}$ ?

Possible Answers:

$3*\sqrt{3}$

$4*\sqrt{3}$

$3*\sqrt{2}$

$2*\sqrt{3}$

$2*\sqrt{2}$

Correct answer:

$2*\sqrt{2}$

Explanation:

To find an equivalency we must rationalize the denominator.

To rationalize the denominator multiply the numerator and denominator by the denominator.

$\frac{12}{\sqrt{18}}*\frac{\sqrt{18}}{\sqrt{18}}=$

$\frac{12*\sqrt{18}}{18}=$

Factor out 6,

$\frac{2*\sqrt{18}}{3}=$

Extract perfect square 9 from the square root of 18.

$\sqrt{18}=3*\sqrt{2}$

$\frac{2*3*\sqrt{2}}{3}=$

$2*\sqrt{2}$

Report an Error

View ACT Math Tutors

Mridul
Certified Tutor

Indian Institute Of Technology Delhi, Bachelor, Production and Industrial Engineering.

View ACT Math Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

View ACT Math Tutors

Joseph
Certified Tutor

University of Wisconsin Colleges, Bachelor in Arts, Mathematics.

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

Popular Courses & Classes

Spanish Courses & Classes in Houston, ISEE Courses & Classes in Phoenix, MCAT Courses & Classes in Washington DC, GMAT Courses & Classes in Philadelphia, SAT Courses & Classes in Los Angeles, Spanish Courses & Classes in New York City, MCAT Courses & Classes in Seattle, SSAT Courses & Classes in Phoenix, GMAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in San Francisco-Bay Area

Popular Test Prep

SAT Test Prep in Houston, MCAT Test Prep in Boston, SAT Test Prep in Miami, SSAT Test Prep in Seattle, SSAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Houston, SSAT Test Prep in Boston, MCAT Test Prep in Washington DC, GRE Test Prep in Dallas Fort Worth, SAT Test Prep in Denver

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

ACT Math : How to factor a common factor out of squares

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Factor A Common Factor Out Of Squares

Example Question #2 : How To Factor A Common Factor Out Of Squares

Example Question #1 : Factoring Squares

Example Question #1 : How To Factor A Common Factor Out Of Squares

Example Question #5 : How To Factor A Common Factor Out Of Squares

Example Question #6 : How To Factor A Common Factor Out Of Squares

Example Question #2321 : Act Math

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: