Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Multiplying and Dividing 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 #21 : Multiplying And Dividing Radicals

Simply this radical: $\sqrt{6}\sqrt{8}\sqrt{10}$

Possible Answers:

$2\sqrt{30}$

None of the other answers.

$\sqrt{30}$

$4\sqrt{15}$

$4\sqrt{30}$

Correct answer:

$4\sqrt{30}$

Explanation:

If you do not immediately see a perfect square within a number then break it down into smaller numbers. Then select from those a perfect square to be removed. When multiplying radicals it is easiest to start by combining them all under one radical.

$\sqrt{6}\sqrt{8}\sqrt{10}$

combine under one roof:

$\sqrt{6*8*10}$

now break apart each number into its factors

$\sqrt{2*3*2*2*2*5}$ now you can see perfect squares that were otherwise not there. Remove perfect squares. For example two 2's makes 4 which is a perfect square...

$4\sqrt{2*3*5}$

simplify under the radical

$4\sqrt{30}$

Report an Error

Example Question #4114 : Algebra Ii

Simplify.

$\sqrt{2}(\sqrt{3}-\sqrt{5})$

Possible Answers:

$3\sqrt{5}$

$5\sqrt{3}$

$\sqrt{6}-\sqrt{10}$

$2\sqrt{10}$

Correct answer:

$\sqrt{6}-\sqrt{10}$

Explanation:

$\sqrt{2}(\sqrt{3}-\sqrt{5})$ Distribute. When multiplying radicals, you can combine them and multiply the numbers inside the radical.

$\sqrt{6}-\sqrt{10}$

Report an Error

Example Question #4112 : Algebra Ii

Multilpy and simplify: $\sqrt{12x}\cdot \sqrt{3x^2y}$

Possible Answers:

$6x\sqrt{x}$

$x\sqrt{xy}$

$6x\sqrt{xy}$

$6\sqrt{xy}$

$6x\sqrt{y}$

Correct answer:

$6x\sqrt{xy}$

Explanation:

Multiply and simplify: $\sqrt{12x}\cdot \sqrt{3x^2y}$ . I like to multiply everything and put it all underneath one big radical first: $\sqrt{36x^3y}$ . Then, simplify each term separately. factors to $3\cdot 3\cdot 2\cdot 2$ . When dealing with square roots, for every pair of the same number, you cross the pair out and put one of those numbers outside of the radicals. The loners remain underneath the radical. Therefore, $\sqrt{36}=6$ . Do the same with the and terms. Therefore, your answer is: $6x\sqrt{xy}$ .

Report an Error

Example Question #21 : Multiplying And Dividing Radicals

Simplify.

$\frac{\sqrt{12}}{\sqrt{6}}$

Possible Answers:

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

$\sqrt{6}$

$\sqrt{2}$

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

Correct answer:

$\sqrt{2}$

Explanation:

When dividing radicals, we can try to simplify it by combining the radicals.

$\frac{\sqrt{12}}{\sqrt{6}}=\sqrt{\frac{12}{6}}=\sqrt{2}$

Report an Error

Example Question #22 : Multiplying And Dividing Radicals

Simplify.

$\frac{\sqrt{24}}{\sqrt{2}}$

Possible Answers:

$2\sqrt{3}$

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

$3\sqrt{2}$

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

Correct answer:

$2\sqrt{3}$

Explanation:

When dividing radicals, we can try to simplify it by combining the radicals.

$\frac{\sqrt{24}}{\sqrt{2}}=\sqrt{\frac{24}{2}}=\sqrt{12}=2\sqrt{3}$ Remember to factor out the square and that's how you can complete the simplification.

Report an Error

Example Question #23 : Multiplying And Dividing Radicals

Simplify.

$\sqrt{5}\cdot\sqrt{2}$

Possible Answers:

$\sqrt{7}$

$\sqrt{10}$

$2\sqrt{5}$

$5\sqrt{2}$

Correct answer:

$\sqrt{10}$

Explanation:

When multiplying radicals, you can combine them and multiply the numbers inside the radical.

$\sqrt{5}\cdot\sqrt{2}=\sqrt{5\cdot2}=\sqrt{10}$

Report an Error

Example Question #27 : Multiplying And Dividing Radicals

Simplify.

$\sqrt{6}\cdot3\sqrt{6}$

Possible Answers:

$4\sqrt{6}$

$6\sqrt{3}$

Correct answer:

Explanation:

$\sqrt{6}\cdot3\sqrt{6}$ When multiplying radicals, you can combine them and multiply the numbers inside the radical. NUmbers outside the radical are also multiplied.

$3\sqrt{36}$ We can simplify this.

$3\cdot6=18$

Report an Error

Example Question #25 : Multiplying And Dividing Radicals

Simplify.

$\sqrt{6}\cdot\sqrt{3}$

Possible Answers:

$\sqrt{18}$

$3\sqrt{2}$

$9\sqrt{2}$

$2\sqrt{3}$

Correct answer:

$3\sqrt{2}$

Explanation:

$\sqrt{6}\cdot\sqrt{3}$ When multiplying radicals, you can combine them and multiply the numbers inside the radical.

$\sqrt{18}$ We can simplify this. Lets find a perfect square.

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

Report an Error

Example Question #29 : Multiplying And Dividing Radicals

Simplify.

$\frac{\sqrt{24}}{4}$

Possible Answers:

$\frac{\sqrt{6}}{2}$

$\frac{\sqrt{6}}{4}$

$\frac{\sqrt{2}}2{}$

$\frac{\sqrt{24}}4{}$

Correct answer:

$\frac{\sqrt{6}}{2}$

Explanation:

When dividing radicals with an integer, let's simplify the radical. We need to find a perfect square.

$\frac{\sqrt{24}}{4}=\frac{\sqrt{4}\cdot\sqrt{6}}{4}=\frac{2\sqrt{6}}{4}$ . We can reduce.

$\frac{2\sqrt{6}}{4}=\frac{\sqrt{6}}{2}$

Report an Error

Example Question #30 : Multiplying And Dividing Radicals

Simplify.

$\frac{\sqrt{48}}{16}$

Possible Answers:

$\frac{\sqrt{3}}4{}$

$4\sqrt{3}$

$2\sqrt{3}$

$\sqrt{3}$

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

Correct answer:

$\frac{\sqrt{3}}4{}$

Explanation:

When dividing radicals with an integer, let's simplify the radical. We need to find a perfect square.

$\frac{\sqrt{48}}{16}=\frac{\sqrt{16}\cdot\sqrt{3}}{16}=\frac{4\sqrt{3}}{16}$ . We can reduce.

$\frac{4\sqrt{3}}{16}=\frac{\sqrt{3}}{4}$

Report an Error

View Algebra 2 Tutors

Emmanuel
Certified Tutor

Baylor University, Bachelor of Science, Biology, General.

View Algebra 2 Tutors

Alejandro
Certified Tutor

Kennesaw State University, Bachelor of Science, Computer Software Engineering.

View Algebra 2 Tutors

Allison
Certified Tutor

Asbury University, Bachelor of Education, Mathematics Teacher Education.

All Algebra II Resources

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

Popular Subjects

Computer Science Tutors in Washington DC, Biology Tutors in San Francisco-Bay Area, Statistics Tutors in Houston, GMAT Tutors in Chicago, Chemistry Tutors in Chicago, English Tutors in New York City, Math Tutors in Miami, SAT Tutors in New York City, English Tutors in Washington DC, Math Tutors in Phoenix

Popular Courses & Classes

ACT Courses & Classes in Atlanta, GRE Courses & Classes in Washington DC, SAT Courses & Classes in Philadelphia, ACT Courses & Classes in Philadelphia, ACT Courses & Classes in Phoenix, MCAT Courses & Classes in Chicago, LSAT Courses & Classes in Denver, ISEE Courses & Classes in Denver, ACT Courses & Classes in Denver, SAT Courses & Classes in Houston

Popular Test Prep

MCAT Test Prep in Philadelphia, SSAT Test Prep in Denver, GMAT Test Prep in Miami, SAT Test Prep in Miami, ACT Test Prep in Atlanta, LSAT Test Prep in Chicago, ACT Test Prep in Denver, GRE Test Prep in Washington DC, SSAT Test Prep in Seattle, MCAT Test Prep in Chicago

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 : Multiplying and Dividing Radicals

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #21 : Multiplying And Dividing Radicals

Example Question #4114 : Algebra Ii

Example Question #4112 : Algebra Ii

Example Question #21 : Multiplying And Dividing Radicals

Example Question #22 : Multiplying And Dividing Radicals

Example Question #23 : Multiplying And Dividing Radicals

Example Question #27 : Multiplying And Dividing Radicals

Example Question #25 : Multiplying And Dividing Radicals

Example Question #29 : Multiplying And Dividing Radicals

Example Question #30 : Multiplying And Dividing Radicals

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: