Call Now to Set Up Tutoring:

(888) 888-0446

GED Math : Square Roots and Radicals

Study concepts, example questions & explanations for GED Math

Create An Account

All GED Math Resources

4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Square Roots And Radicals

Simplify:
$\small \sqrt{192}$

Possible Answers:

$\small 4\sqrt{12}$

$\small 64\sqrt3$

$\small 16\sqrt{12}$

$\small \small 8\sqrt3$

Correct answer:

$\small \small 8\sqrt3$

Explanation:

$\small \sqrt{192}=\sqrt{64}\times \sqrt3=8\times \sqrt3=8\sqrt3$

An alternate solution is:

$\small \sqrt{192}=\sqrt{16}\times \sqrt{12}=4\times \sqrt{4} \times \sqrt3=4\times2\times\sqrt3=8\sqrt3$

Report an Error

Example Question #2 : Square Roots And Radicals

Simplify:

$\small \sqrt{x^4}$

Possible Answers:

$\small x^3$

$\small \sqrt{x^4}$

$\small x^2$

$\small x$

Correct answer:

$\small x^2$

Explanation:

$\small \sqrt{x^4}=\sqrt{x^2}\times \sqrt{x^2}=x\times x=x^2$

Report an Error

Example Question #3 : Square Roots And Radicals

Simplify:

$\small \sqrt{98}$

Possible Answers:

$\small 49\sqrt2$

$\small 4\sqrt7$

$\small 7\sqrt2$

$\small 2\sqrt7$

Correct answer:

$\small 7\sqrt2$

Explanation:

$\small \sqrt{98}=\sqrt{49}\times \sqrt{2}=7\times \sqrt2=7\sqrt2$

Report an Error

Example Question #4 : Square Roots And Radicals

Simplify:

$\small \sqrt{72}=$

Possible Answers:

$\small 6\sqrt2$

$\small 2\sqrt6$

$\small 4\sqrt6$

$\small 36\sqrt2$

Correct answer:

$\small 6\sqrt2$

Explanation:

$\small \sqrt{72}=\sqrt{36}\times \sqrt2=6\times \sqrt2=6\sqrt2$

Report an Error

Example Question #2 : Square Roots And Radicals

Simplify:

$\sqrt{147}$

Possible Answers:

$9\sqrt7$

$7\sqrt3$

$3\sqrt7$

$49\sqrt3$

Correct answer:

$7\sqrt3$

Explanation:

$\sqrt{147}=\sqrt{49}\times \sqrt3=7\times \sqrt3=7\sqrt3$

Report an Error

Example Question #6 : Square Roots And Radicals

Numberline_1

Refer to the above number line. What point most likely represents the square root of 280?

Do not use a calculator.

Possible Answers:

Correct answer:

Explanation:

$16^{2} = 256 < 280 < 289 < 17^{2}$

Therefore, $16 < \sqrt{280} < 17$ ,

making the correct choice .

Report an Error

Example Question #3 : Square Roots And Radicals

Simplify:

$\sqrt{48}$

Do not use a calculator.

Possible Answers:

$6\sqrt{2}$

$3 \sqrt{6}$

$4\sqrt{3}$

The expression is in simplest form.

Correct answer:

$4\sqrt{3}$

Explanation:

The prime factorization of 48 is

$48 = 2 \times 2 \times 2 \times 2 \times 3$ .

Rewrite, and use the product of radicals property to simplify:

$\sqrt{48}$

$= \sqrt{ 2 \times 2 \times 2 \times 2 \times 3}$

$= \sqrt{ 2 \times 2 } \times \sqrt{ 2 \times 2 } \times \sqrt{ 3}$

$= 2 \times 2 \times \sqrt{ 3}$

$=4 \sqrt{ 3}$

Report an Error

Example Question #3 : Square Roots And Radicals

Simplify:

$\sqrt{42}$

Do not use a calculator.

Possible Answers:

$3 \sqrt{7}$

The expression is in simplest form.

$7 \sqrt{2}$

$2 \sqrt{7}$

Correct answer:

The expression is in simplest form.

Explanation:

The prime factorization of 42 is

$42 = 2 \times 3 \times 7$ .

Since 42 is the product of distinct primes, it has no perfect square factors, and, therefore, its square root cannot be simplified further. It is already in simplifed form.

Report an Error

Example Question #6 : Square Roots And Radicals

Factor: $2\sqrt{120}$

Possible Answers:

$24\sqrt5$

$24\sqrt{10}$

$4\sqrt{30}$

$12\sqrt{10}$

$2\sqrt{15}$

Correct answer:

$4\sqrt{30}$

Explanation:

In order to factor the radical, we will need to rewrite 120 as multiples of perfect squares.

$2\sqrt{120} = 2\sqrt{30} \cdot \sqrt{4}$

Reduce the known term

$2\sqrt{30} \cdot \sqrt{4} =2\sqrt{30} \cdot 2 = 4\sqrt{30}$

The value of $\sqrt{30}$ cannot be factored any further.

The answer is: $4\sqrt{30}$

Report an Error

Example Question #1 : Square Roots And Radicals

Factor: $6\sqrt{40}$

Possible Answers:

$24\sqrt{10}$

$2\sqrt{30}$

$40\sqrt{3}$

$12\sqrt{10}$

$\textup{The expression is already factored.}$

Correct answer:

$12\sqrt{10}$

Explanation:

Rewrite the root 40 in factors of perfect squares.

$6\sqrt{40} = 6 \cdot \sqrt{4}\cdot \sqrt{10} = 6 \cdot 2\cdot \sqrt{10}$

The answer is: $12\sqrt{10}$

Report an Error

View Tutors

Abhisek
Certified Tutor

University of Florida, Bachelor of Engineering, Computer Science.

View Tutors

Alyce
Certified Tutor

The University of Alabama, Master of Arts, German.

View Tutors

Roberto
Certified Tutor

Conservatorio Nacional de Musica, Bachelor in Arts, Music Performance. CUNY Hunter College, Master of Arts, Music Performance.

All GED Math Resources

4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ACT Tutors in Atlanta, GMAT Tutors in Chicago, SAT Tutors in Washington DC, Statistics Tutors in Dallas Fort Worth, SSAT Tutors in Washington DC, Math Tutors in Washington DC, SSAT Tutors in San Diego, ISEE Tutors in Miami, Chemistry Tutors in Dallas Fort Worth, Spanish Tutors in Seattle

Popular Courses & Classes

Spanish Courses & Classes in Chicago, Spanish Courses & Classes in Los Angeles, LSAT Courses & Classes in San Diego, ISEE Courses & Classes in Miami, MCAT Courses & Classes in Philadelphia, SSAT Courses & Classes in Houston, SAT Courses & Classes in Boston, LSAT Courses & Classes in Chicago, GRE Courses & Classes in Denver, Spanish Courses & Classes in Washington DC

Popular Test Prep

ISEE Test Prep in Denver, MCAT Test Prep in Philadelphia, SAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Atlanta, MCAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Atlanta, ISEE Test Prep in New York City, SAT Test Prep in Atlanta, ISEE Test Prep in Miami, LSAT Test Prep in Atlanta

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

GED Math : Square Roots and Radicals

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #1 : Square Roots And Radicals

Example Question #2 : Square Roots And Radicals

Example Question #3 : Square Roots And Radicals

Example Question #4 : Square Roots And Radicals

Example Question #2 : Square Roots And Radicals

Example Question #6 : Square Roots And Radicals

Example Question #3 : Square Roots And Radicals

Example Question #3 : Square Roots And Radicals

Example Question #6 : Square Roots And Radicals

Example Question #1 : Square Roots And Radicals

All GED Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: