We are open Saturday and Sunday!

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

← Previous 1 2 3 4 5 6 7 Next →

Example Question #1 : Multiplying And Dividing Radicals

Multiply and express the answer in the simplest form:

$\small \sqrt3(\sqrt4-\sqrt3)$

Possible Answers:

$\small 2\sqrt3-3$

$\small 4\sqrt3-9$

$\small \sqrt{12}-\sqrt9$

$\small \sqrt7-\sqrt6$

Correct answer:

$\small 2\sqrt3-3$

Explanation:

$\small \sqrt3(\sqrt4-\sqrt3)$

$\small \sqrt{12}-\sqrt9$

$\small \sqrt{12}=\sqrt4 \times \sqrt3=2\sqrt3$

$\small \sqrt9=3$

$\small \sqrt{12}-\sqrt9=2\sqrt3-3$

Report an Error

Example Question #1 : Multiplying And Dividing Radicals

$\left ( \sqrt{x}+\sqrt{6} \right )\left ( \sqrt{x}-\sqrt{6} \right )$

Possible Answers:

$\sqrt{x}-6$

$x-\sqrt{6}$

x-6

$x^{2}-36$

$x-\sqrt{12}$

Correct answer:

x-6

Explanation:

FOIL with difference of squares. The multiplying cancels the square roots on both terms.

Report an Error

Example Question #1 : Multiplying And Dividing Radicals

Simplify.

$\sqrt{36} \times 3\sqrt{36}$

Possible Answers:

108

$3\sqrt{36}$

$4\sqrt{36}$

Correct answer:

108

Explanation:

We can solve this by simplifying the radicals first: $\sqrt{36} =6$

Plugging this into the equation gives us:

$6 \times3(6)=108$

Report an Error

Example Question #2 : Multiplying And Dividing Radicals

Simplify.

$5\sqrt{2} \times4\sqrt{2}$

Possible Answers:

$20\sqrt{2}$

$\sqrt{80}$

Correct answer:

Explanation:

Note: the product of the radicals is the same as the radical of the product:

$\sqrt{2} \times \sqrt2} = \sqrt{2\times 2$ which is $\sqrt{4} =2$

Once we understand this, we can plug it into the equation:

$5\sqrt{2} \times4\sqrt{2} = 5\times4\times \sqrt{2\times 2}$

$5\times4\times2=40$

Report an Error

Example Question #3 : Multiplying And Dividing Radicals

Simplify.

$\frac{\sqrt{32}}{3\sqrt{16}}$

Possible Answers:

$\frac{4}{12}$

$\sqrt{2}$

$\frac{4\sqrt{2}}{12}$

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

Correct answer:

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

Explanation:

We can simplify the radicals:

$\sqrt{32} =\sqrt{16\times 2} =4\sqrt{2}$ and $\sqrt{16} =4$

Plug in the simplifed radicals into the equation:

$\frac{4\sqrt{2}}{3\times 4} = \frac{4\sqrt{2}}{12}$

$\frac{4 \sqrt2}{12}=\frac{\sqrt2}{3}$

Report an Error

Example Question #4 : Multiplying And Dividing Radicals

Simplify and rationalize the denominator if needed,

$\frac{\sqrt{16}}{4\sqrt{2}}$

Possible Answers:

$\sqrt{2}$

$\frac{\sqrt2}{2}$

$\frac{1}{2}$

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

Correct answer:

$\frac{\sqrt2}{2}$

Explanation:

We can only simplify the radical in the numerator: $\sqrt{16} =4$

Plugging in the simplifed radical into the equation we get:

$\frac{4}{4\sqrt{2}} = \frac{1}{\sqrt{2}}$

Note: We simplified further because both the numerator and denominator had a "4" which canceled out.

Now we want to rationalize the denominator,

$\frac{1}{\sqrt2}\bigg(\frac{\sqrt2}{\sqrt2}\bigg)=\frac{\sqrt2}{2}$

Report an Error

Example Question #2 : Multiplying And Dividing Radicals

Simplify $2x^{2}\cdot x^{5}\cdot 3x^{3}$

Possible Answers:

$5x^{10}$

$6x^{13}$

$6x^{30}$

$5x^{30}$

$6x^{10}$

Correct answer:

$6x^{10}$

Explanation:

To simplify, you must use the Law of Exponents.

First you must multiply the coefficients then add the exponents:

$2\cdot3\cdot x^{2+5+3}=6\cdot x^{10}=6x^{10}$ .

Report an Error

Example Question #1 : Multiplying And Dividing Radicals

What is the product of $\sqrt{12}$ and $3\sqrt{6}$ ?

Possible Answers:

$18\sqrt{2}$

$3\sqrt{72}$

$6\sqrt{18}$

$9\sqrt{24}$

$12\sqrt{18}$

Correct answer:

$18\sqrt{2}$

Explanation:

First, simplify $\sqrt{12}=\sqrt{4\cdot3}$ to $2\sqrt{3}$ .

Then set up the multiplication problem:

$2\sqrt{3}\cdot 3\sqrt{6}$ .

Multiply the terms outside of the radical, then the terms under the radical:

$2\cdot 3\sqrt{3\cdot6}$ then simplfy: $6\sqrt{18}.$

The radical is still not in its simplest form and must be reduced further:

$6\sqrt{18}=6\cdot3\sqrt{2}=18\sqrt{2}$ . This is the radical in its simplest form.

Report an Error

Example Question #6 : Multiplying And Dividing Radicals

Simplify

${}\frac{\sqrt{117}}{\sqrt{13}}$

Possible Answers:

$3\sqrt{13}$

$\sqrt9$

$3\sqrt9$

$\sqrt{13}$

Correct answer:

Explanation:

To divide the radicals, simply divide the numbers under the radical and leave them under the radical:

$\sqrt{\frac{117}{13}}=\sqrt9$

Then simplify this radical:

$\sqrt9=3$ .

Report an Error

Example Question #1 : Multiplying And Dividing Radicals

Solve and simplify.

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

Possible Answers:

$\sqrt{7}$

$\sqrt{5}$

$\sqrt{23}$

$\sqrt{6}$

Correct answer:

$\sqrt{6}$

Explanation:

When multiplying radicals, just take the values inside the radicand and perfom the operation.

$\sqrt{2}\cdot \sqrt{3}=\sqrt{2\cdot 3}=\sqrt{6}$

$\sqrt{6}$ can't be reduced so this is the final answer.

Report an Error

← Previous 1 2 3 4 5 6 7 Next →

View Algebra 2 Tutors

Sekou
Certified Tutor

University of New Haven, Bachelor in Arts, Mathematics.

View Algebra 2 Tutors

Jeromy
Certified Tutor

Washington State University, Bachelor of Science, Psychology. University of Washington-Seattle Campus, Master of Arts Teachin...

View Algebra 2 Tutors

Carolyn
Certified Tutor

University of California-Los Angeles, Bachelor in Arts, Mathematics.

All Algebra II Resources

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

Popular Subjects

Reading Tutors in Boston, GRE Tutors in Seattle, Statistics Tutors in Los Angeles, LSAT Tutors in Washington DC, Spanish Tutors in Los Angeles, Chemistry Tutors in Philadelphia, English Tutors in Los Angeles, French Tutors in New York City, French Tutors in Philadelphia, GRE Tutors in Los Angeles

Popular Courses & Classes

ISEE Courses & Classes in Phoenix, GRE Courses & Classes in Phoenix, SSAT Courses & Classes in New York City, LSAT Courses & Classes in Philadelphia, MCAT Courses & Classes in Seattle, LSAT Courses & Classes in Miami, GRE Courses & Classes in New York City, SSAT Courses & Classes in Washington DC, GRE Courses & Classes in Houston, SAT Courses & Classes in Washington DC

Popular Test Prep

GRE Test Prep in Atlanta, LSAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Miami, ISEE Test Prep in Phoenix, GMAT Test Prep in Boston, ACT Test Prep in New York City, GRE Test Prep in Miami, ACT Test Prep in Chicago, SSAT Test Prep in Boston, LSAT Test Prep in New York City

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 #1 : Multiplying And Dividing Radicals

Example Question #1 : Multiplying And Dividing Radicals

Example Question #1 : Multiplying And Dividing Radicals

Example Question #2 : Multiplying And Dividing Radicals

Example Question #3 : Multiplying And Dividing Radicals

Example Question #4 : Multiplying And Dividing Radicals

Example Question #2 : Multiplying And Dividing Radicals

Example Question #1 : Multiplying And Dividing Radicals

Example Question #6 : Multiplying And Dividing Radicals

Example Question #1 : 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: