Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Adding and Subtracting Radicals

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #91 : Simplifying Radicals

Add the radicals, if possible: $\sqrt{18}+\sqrt{50}+\sqrt{200}$

Possible Answers:

$9 \sqrt{3}$

$18 \sqrt{2}$

$\textup{The radicals cannot be added.}$

$24 \sqrt{2}$

$6\sqrt3$

Correct answer:

$18 \sqrt{2}$

Explanation:

Simplify all the radicals to their simplest forms. Use the perfect squares as the factors.

$\sqrt{18} =\sqrt{9\times 2}= \sqrt{9}\cdot \sqrt{2} = 3\sqrt{2}$

$\sqrt{50}= \sqrt{25}\cdot \sqrt{2} = 5 \sqrt{2}$

$\sqrt{200} = \sqrt{100}\cdot \sqrt{2} = 10\sqrt2$

Add the like terms together.

$3 \sqrt{2}+5 \sqrt{2}+10 \sqrt{2} = 18 \sqrt{2}$

The answer is: $18 \sqrt{2}$

Report an Error

Example Question #91 : Simplifying Radicals

Simplify: $\sqrt{4x^2}-\sqrt{16y^4}$

Possible Answers:

2x^2-8y^2

12x-8y^2

2x-16y^2

2x-8y

2x-4y^2

Correct answer:

2x-4y^2

Explanation:

Simplify each radical first.

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

$\sqrt{16y^4}=4y^2$

Now, subtract those:

2x-4y^2

Report an Error

Example Question #1431 : Mathematical Relationships And Basic Graphs

Add the radicals, if possible: $\sqrt8+\sqrt{20}+\sqrt{50}$

Possible Answers:

$7\sqrt3+2\sqrt6$

$7\sqrt5+2\sqrt2$

$\textup{The terms cannot be simplified.}$

$7\sqrt2+2\sqrt5$

Correct answer:

$7\sqrt2+2\sqrt5$

Explanation:

Rewrite the radicals using common factors of perfect squares.

$\sqrt8+\sqrt{20}+\sqrt{50} = \sqrt{4\times2}+\sqrt{4\times 5}+\sqrt{25\times 2}$

The equation becomes:

$\sqrt{4\times2}+\sqrt{4\times 5}+\sqrt{25\times 2}= 2\sqrt2+2\sqrt5 + 5\sqrt2$

Combine like-terms.

The answer is: $7\sqrt2+2\sqrt5$

Report an Error

Example Question #101 : Simplifying Radicals

Add the radicals, if possible: $2\sqrt{27}+4\sqrt{24}+3\sqrt{12}$

Possible Answers:

$4\sqrt3+9\sqrt6$

$\textup{The radicals are already simplified.}$

$12\sqrt3+8\sqrt6$

$6\sqrt3+9\sqrt6$

$5\sqrt3+2\sqrt6$

Correct answer:

$12\sqrt3+8\sqrt6$

Explanation:

Evaluate each square root by factoring each with factors of perfect squares.

$\sqrt{27}= \sqrt{9}\cdot \sqrt 3 = 3\sqrt3$

$\sqrt{24} = \sqrt{4}\cdot \sqrt 6 = 2\sqrt6$

$\sqrt{12} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt3$

Replace all the terms in the expression.

$2\sqrt{27}+4\sqrt{24}+3\sqrt{12} = 2(3\sqrt3)+4(2\sqrt6)+3(2\sqrt{3})$

$6\sqrt3+8\sqrt6+6\sqrt3 = 12\sqrt3+8\sqrt6$

The answer is: $12\sqrt3+8\sqrt6$

Report an Error

Example Question #1433 : Mathematical Relationships And Basic Graphs

Add the radicals, if possible: $2\sqrt3+\sqrt6 +\sqrt{12}$

Possible Answers:

$2\sqrt2 +2\sqrt3$

$8\sqrt2 +\sqrt6$

$\textup{The radicals are already simplified.}$

$2\sqrt6 +2\sqrt3$

$4\sqrt3 +\sqrt6$

Correct answer:

$4\sqrt3 +\sqrt6$

Explanation:

Every radical in this expression is simplified except $\sqrt{12}$ .

Simplify by rewriting this radical using factors of perfect squares.

$\sqrt{12} = \sqrt{4}\cdot \sqrt{3} = 2\sqrt3$

Replace the term.

$2\sqrt3+\sqrt6 +\sqrt{12}=2\sqrt3+\sqrt6 +2\sqrt3$

Combine like-terms.

The answer is: $4\sqrt3 +\sqrt6$

Report an Error

Example Question #56 : Adding And Subtracting Radicals

Simplify the expression:

$\sqrt{72} + \sqrt{98} - \sqrt{2}$

Possible Answers:

$4 \sqrt{21}$

$2\sqrt{42}$

$6\sqrt{14}$

$13\sqrt{2}$

$12\sqrt{2}$

Correct answer:

$12\sqrt{2}$

Explanation:

Simplify each of the three square root terms separately. Simplify $\sqrt{72}$ first as follows:

Express radicand 72 as the product of its prime factors:

$72 = 2 \cdot 36$

$= 2 \cdot 2 \cdot 18$

$= 2 \cdot 2 \cdot 2 \cdot 9$

$= 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$

Look for any prime factors that appear twice; there are two, 2 and 3, so restate the radical as

$\sqrt{72}$

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

$= \sqrt{ 2 ^{2} \cdot 3 ^{2} \cdot 2}$

By the Product of Radicals Property, we can restate this as

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

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

$=6 \sqrt{ 2}$

The second term, $\sqrt{98}$ , can be simplified similarly:

$98 = 2 \cdot 49$

$= 2 \cdot 7 \cdot 7$

$\sqrt{98}$

$= \sqrt{2 \cdot 7 \cdot 7}$

$= \sqrt{ 7 ^{2}\cdot 2 }$

$= \sqrt{ 7 ^{2} } \cdot \sqrt{2}$

$= 7\sqrt{2}$

The third term, $\sqrt{2}$ , is already simplified, as 2 is prime.

Therefore,

$\sqrt{72} + \sqrt{98} - \sqrt{2}$

can be rewritten, and simplified using distribution:

$6 \sqrt{2} + 7 \sqrt{2} -1 \sqrt{2}$

$=( 6 + 7 -1 )\sqrt{2}$

$= 12 \sqrt{2}$

Report an Error

View Algebra 2 Tutors

Abe
Certified Tutor

CUNY Brooklyn College, Bachelor of Science, Accounting and Business Management. CUNY Graduate School and University Center, M...

View Algebra 2 Tutors

Brandon
Certified Tutor

Flager College, Bachelor, Elementary Education .

View Algebra 2 Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Reading Tutors in San Francisco-Bay Area, Computer Science Tutors in New York City, Spanish Tutors in Chicago, Physics Tutors in San Francisco-Bay Area, SAT Tutors in Dallas Fort Worth, Computer Science Tutors in Phoenix, GRE Tutors in San Diego, Math Tutors in Denver, SSAT Tutors in Chicago, Computer Science Tutors in Atlanta

Popular Courses & Classes

SSAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in New York City, ISEE Courses & Classes in Seattle, ISEE Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Boston, LSAT Courses & Classes in Philadelphia, ACT Courses & Classes in Denver, SAT Courses & Classes in Chicago, LSAT Courses & Classes in Chicago

Popular Test Prep

GMAT Test Prep in Miami, MCAT Test Prep in New York City, LSAT Test Prep in Philadelphia, SAT Test Prep in Los Angeles, GMAT Test Prep in San Diego, SSAT Test Prep in Philadelphia, SAT Test Prep in Philadelphia, ISEE Test Prep in Chicago, MCAT Test Prep in Seattle, ACT Test Prep in Los Angeles

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

Algebra II : Adding and Subtracting Radicals

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #91 : Simplifying Radicals

Example Question #91 : Simplifying Radicals

Example Question #1431 : Mathematical Relationships And Basic Graphs

Example Question #101 : Simplifying Radicals

Example Question #1433 : Mathematical Relationships And Basic Graphs

Example Question #56 : Adding And Subtracting Radicals

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: