We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Simplifying 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 #13 : Multiplying And Dividing Radicals

Solve and simplify.

$(4\sqrt{7})^2$

Possible Answers:

784

112

Correct answer:

112

Explanation:

Since we are dealing with exponents, lets break it down.

$(4{\sqrt{7}})^2=4^2\cdot ({\sqrt{7}})^2=16\cdot 7=112$

Remember to distribute.

Report an Error

Example Question #18 : Multiplying And Dividing Radicals

Solve and simplify.

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

Possible Answers:

$3\sqrt{2}$

$\sqrt{2}$

$2\sqrt{3}$

Correct answer:

$2\sqrt{3}$

Explanation:

When dividing radicals, check the denominator to make sure it can be simplified or that there is a radical present that needs to be fixed. Since there is a radical present, we need to eliminate that radical. However, there is a faster way to possibly elminate the denominator. Let's simplify the numerator.

$\sqrt{24}=\sqrt{8\cdot3}=\sqrt{4\cdot2\cdot3}=2\sqrt{2}\cdot\sqrt{3}$ .

The reason I split it up is because I can cancel out the radicals and thus simplifying the question to give final answer of $2\sqrt{3}$ .

Report an Error

Example Question #19 : Multiplying And Dividing Radicals

Solve and simplify.

$\frac{2\sqrt{75}}{3\sqrt{175}}$

Possible Answers:

$3\sqrt{2}$

$\frac{7\sqrt{21}}{2}$

$\frac{2\sqrt{21}}{21}$

Correct answer:

$\frac{2\sqrt{21}}{21}$

Explanation:

$\frac{2\sqrt{75}}{3\sqrt{175}}=\frac{2\cdot\sqrt{25\cdot3}}{3\cdot\sqrt{25\cdot7}}=\frac{2\cdot\sqrt{25}\cdot\sqrt{3}}{3\cdot\sqrt{25}\cdot\sqrt{7}}=\frac{2\sqrt{3}}{3\sqrt{7}}$

We still need to eliminate the radical so multiply top and bottom by $\sqrt{7}$ .

$\frac{2\sqrt{3}\cdot\sqrt{7}}{3\sqrt{7}\cdot\sqrt{7}}=\frac{2\sqrt{21}}{3\cdot 7}=\frac{2\sqrt{21}}{21}$ .

Report an Error

Example Question #20 : Multiplying And Dividing Radicals

Multiply and simplify:

$\sqrt{12x}\cdot \sqrt{3x^4}$ .

Possible Answers:

$\sqrt{x}$

$x^2\sqrt{x}$

$x^2\sqrt{6x}$

$6x\sqrt{x}$

$6x^2\sqrt{x}$

Correct answer:

$6x^2\sqrt{x}$

Explanation:

I would first multiply and put everything under the radical to then figure out what to simplify.

After mulitplying everything together, it should look like:

$\sqrt{36x^5}$ .

Then, simplify.

is a perfect square, and for every pair of x's, put one on the outside and cross out the pair.

We are left with an answer of:

$6x^2\sqrt{x}$ .

Report an Error

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 #211 : Radicals

Simplify.

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

Possible Answers:

$2\sqrt{10}$

$3\sqrt{5}$

$5\sqrt{3}$

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

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:

$\sqrt{2}$

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

$\sqrt{6}$

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

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:

$3\sqrt{2}$

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

$2\sqrt{3}$

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

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:

$2\sqrt{5}$

$\sqrt{7}$

$\sqrt{10}$

$5\sqrt{2}$

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

View Algebra 2 Tutors

Fatimah
Certified Tutor

Yarmuke University, Bachelor of Science, Mathematics.

View Algebra 2 Tutors

Chernyeh
Certified Tutor

Purdue University-Main Campus, Bachelor of Science, Business Administration and Management.

View Algebra 2 Tutors

Bhupinder
Certified Tutor

Panjab University, Bachelor of Engineering, Biotechnology. Hamburg University of Technology, Master of Science, Chemical Engi...

All Algebra II Resources

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

Popular Subjects

LSAT Tutors in Atlanta, Calculus Tutors in Phoenix, GRE Tutors in Denver, English Tutors in San Diego, Calculus Tutors in Houston, Computer Science Tutors in Denver, MCAT Tutors in Los Angeles, Reading Tutors in Miami, Chemistry Tutors in Washington DC, Computer Science Tutors in Philadelphia

Popular Courses & Classes

GRE Courses & Classes in Chicago, MCAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Chicago, GRE Courses & Classes in Houston, GRE Courses & Classes in Washington DC, GRE Courses & Classes in Boston, Spanish Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Washington DC, ACT Courses & Classes in Dallas Fort Worth

Popular Test Prep

SAT Test Prep in Denver, GMAT Test Prep in Los Angeles, MCAT Test Prep in Seattle, GRE Test Prep in Miami, ACT Test Prep in Los Angeles, ISEE Test Prep in San Diego, GMAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in New York City, SAT Test Prep in Phoenix, GMAT Test Prep in San Diego

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 : Simplifying Radicals

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #13 : Multiplying And Dividing Radicals

Example Question #18 : Multiplying And Dividing Radicals

Example Question #19 : Multiplying And Dividing Radicals

Example Question #20 : Multiplying And Dividing Radicals

Example Question #21 : Multiplying And Dividing Radicals

Example Question #211 : Radicals

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

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: