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 #31 : Multiplying And Dividing Radicals

Simplify.

$\frac{\sqrt{7}}{\sqrt{5}}$

Possible Answers:

$\frac{5}{7}$

$\frac{7\sqrt{5}}{5}$

$\frac{5\sqrt{7}}{7}$

$\frac{\sqrt{35}}{5}$

$\frac{7}{5}$

Correct answer:

$\frac{\sqrt{35}}{5}$

Explanation:

When dividing radicals, we multiply top and bottom by the bottom radical to ensure our denominator is an integer.

$\frac{\sqrt{7}}{\sqrt{5}}=\frac{\sqrt{7}\cdot\sqrt{5}}{\sqrt{5}\cdot\sqrt{5}}=\frac{\sqrt{35}}{5}$ . This can't be simplified and is our answer.

Report an Error

Example Question #32 : Multiplying And Dividing Radicals

Simplify.

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

Possible Answers:

$\sqrt{3}$

$3\sqrt{3}$

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

Correct answer:

$\sqrt{3}$

Explanation:

When dividing radicals, we multiply top and bottom by the bottom radical to ensure our denominator is an integer.

$\frac{3}{\sqrt{3}}=\frac{3\cdot\sqrt{3}}{\sqrt{3}\cdot\sqrt{3}}=\frac{3\sqrt{3}}{3}=\sqrt{3}$ .

Report an Error

Example Question #33 : Multiplying And Dividing Radicals

Simplify.

$\frac{2}{1+\sqrt{3}}$

Possible Answers:

$-1+\sqrt{3}$

$1-\sqrt{3}$

$-2+2\sqrt{3}$

$\frac{2}{1-\sqrt{3}}$

$\frac{1-\sqrt{3}}{2}$

Correct answer:

$-1+\sqrt{3}$

Explanation:

$\frac{2}{1+\sqrt{3}}$ To get rid of the radical in the denominator, we need to multiply top and bottom by the conjugate which is the opposite sign of the radical expression. This would be $1-\sqrt{3}$ .

$\frac{2}{1+\sqrt{3}}\cdot\frac{1-\sqrt{3}}{1-\sqrt{3}}=\frac{2-2\sqrt{3}}{1-3}=\frac{2-2\sqrt{3}}{-2}$ Remember to FOIL out when multiplying out the denominators. Now, with our answer, we can factor out a .

$\frac{2-2\sqrt{3}}{-2}=\frac{-2(-1+\sqrt{3})}{-2}=-1+\sqrt{3}$

Report an Error

Example Question #4131 : Algebra Ii

Simplify.

$\frac{3}{1-\sqrt{2}}$

Possible Answers:

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

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

$3-3\sqrt{2}$

$3+3\sqrt{2}$

$-3-3\sqrt{2}$

Correct answer:

$-3-3\sqrt{2}$

Explanation:

$\frac{3}{1-\sqrt{2}}$ To get rid of the radical in the denominator, we need to multiply top and bottom by the conjugate which is the opposite sign of the radical expression. This would be $1+\sqrt{2}$ .

$\frac{3}{1-\sqrt{2}}\cdot\frac{1+\sqrt{2}}{1+\sqrt{2}}=\frac{3+3\sqrt{2}}{1-2}=\frac{3+3\sqrt{2}}{-1}$ Remember to use FOIL when multiplying out the denominators. Now, with out answer, we can distribute out the .

$\frac{3+3\sqrt{2}}{-1}=-3-3\sqrt{2}$

Report an Error

Example Question #4132 : Algebra Ii

Multiply: $6\sqrt{3}*2\sqrt{8}$

Possible Answers:

$12\sqrt{6}$

$24\sqrt{6}$

None of these

$12\sqrt{24}$

Cannot combine these radicals

Correct answer:

$24\sqrt{6}$

Explanation:

$6\sqrt{3}*2\sqrt{8}$

Multiply the outer numbers first:

$12(\sqrt{3}*\sqrt{8})$

Combine radicals:

$12\sqrt{24}$

Simplify the radical:

$12\sqrt{6*4}$

$\mathbf{24\sqrt{6}}$

Report an Error

Example Question #33 : Multiplying And Dividing Radicals

$\sqrt{3}*\sqrt{7}$

Possible Answers:

$\sqrt{37}$

$\sqrt{21}$

$\sqrt{10}$

Correct answer:

$\sqrt{21}$

Explanation:

When multiplying radicals, we can just multiply the values inside the radicand.

$\sqrt{3}*\sqrt{7}=\sqrt{3*7}=\sqrt{21}$

Report an Error

Example Question #141 : Simplifying Radicals

$\sqrt{3}*\sqrt{27}$

Possible Answers:

$4\sqrt{3}$

$9\sqrt{3}$

$\sqrt{30}$

Correct answer:

Explanation:

When multiplying radicals, we can just multiply the values inside the radicand.

$\sqrt{3}*\sqrt{27}=\sqrt{3*27}=\sqrt{81}=9$

Report an Error

Example Question #142 : Simplifying Radicals

$\sqrt{5}*\sqrt{15}$

Possible Answers:

$4\sqrt{3}$

$2\sqrt{5}$

$5\sqrt{2}$

$3\sqrt{5}$

$5\sqrt{3}$

Correct answer:

$5\sqrt{3}$

Explanation:

When multiplying radicals, we can just multiply the values inside the radicand.

$\sqrt{5}*\sqrt{15}=\sqrt{5*15}=\sqrt{75}$ We can simplify this by finding a perfect square.

$\sqrt{75}=\sqrt{25}*\sqrt{3}=5\sqrt{3}$

Report an Error

Example Question #143 : Simplifying Radicals

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

Possible Answers:

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

$2\sqrt{2}$

$4\sqrt{2}$

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

Correct answer:

$2\sqrt{2}$

Explanation:

When dealing with radicals in the denominator, we simplify it by multiplying top and bottom by the radical.

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

Report an Error

Example Question #235 : Radicals

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

Possible Answers:

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

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

$\frac{1}{2}$

$\sqrt{2}$

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

Correct answer:

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

Explanation:

We can simplify this fraction. We can combine the radicals into a giant radical expression.

$\frac{\sqrt{6}}{\sqrt{12}}=\sqrt{\frac{6}{12}}=\sqrt{\frac{1}{2}}$

When dealing with radicals in the denominator, we simplify it by multiplying top and bottom by the radical.

$\frac{1}{\sqrt{2}}=\frac{1}{\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}$

Report an Error

View Algebra 2 Tutors

Allison
Certified Tutor

Asbury University, Bachelor of Education, Mathematics Teacher Education.

View Algebra 2 Tutors

Andrew
Certified Tutor

University of Wisconsin-Stevens Point, Bachelor of Science, Mathematics. University of Wisconsin-Oshkosh, Master of Science, ...

View Algebra 2 Tutors

Travis
Certified Tutor

Delaware State University, Bachelor of Science, Mathematics.

All Algebra II Resources

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

Popular Subjects

Biology Tutors in Phoenix, Physics Tutors in Denver, LSAT Tutors in Washington DC, Computer Science Tutors in Phoenix, LSAT Tutors in Dallas Fort Worth, English Tutors in Miami, Physics Tutors in Philadelphia, Physics Tutors in Houston, Statistics Tutors in Denver, Spanish Tutors in Miami

Popular Courses & Classes

Spanish Courses & Classes in Phoenix, GRE Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Philadelphia, GMAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Chicago, SSAT Courses & Classes in San Diego, LSAT Courses & Classes in Boston, Spanish Courses & Classes in Washington DC, ACT Courses & Classes in Seattle, MCAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

MCAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Atlanta, ACT Test Prep in Denver, ISEE Test Prep in San Diego, GRE Test Prep in Boston, ISEE Test Prep in Chicago, SSAT Test Prep in Miami, GRE Test Prep in Miami, GMAT Test Prep in Miami, GRE Test Prep in San Francisco-Bay Area

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 #31 : Multiplying And Dividing Radicals

Example Question #32 : Multiplying And Dividing Radicals

Example Question #33 : Multiplying And Dividing Radicals

Example Question #4131 : Algebra Ii

Example Question #4132 : Algebra Ii

Example Question #33 : Multiplying And Dividing Radicals

Example Question #141 : Simplifying Radicals

Example Question #142 : Simplifying Radicals

Example Question #143 : Simplifying Radicals

Example Question #235 : Radicals

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: