Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Using Radicals with Elementary Operations

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #82 : Algebra Ii

What is the value of $5\sqrt5 + 3 - 4\sqrt{2} +9 - 3\sqrt{5}$ ?

Possible Answers:

$2\sqrt{5} - 4\sqrt{2} + 12$

$2\sqrt{7} - 4\sqrt{7} + 12$

$4\sqrt{7} - 12$

$-2\sqrt{3} + 12$

$2\sqrt{10} - 4\sqrt{2} + 12$

Correct answer:

$2\sqrt{5} - 4\sqrt{2} + 12$

Explanation:

When combining terms involving radicals, we can only combine the ones that have the same radical. For this problem, that means $4\sqrt2$ has to stay on its own while we can combine $5\sqrt5$ and $-3\sqrt5$ into $2\sqrt5$ . The simple integers can be combined too, giving us our answer with three seperate terms.

Report an Error

Example Question #1 : Using Radicals With Elementary Operations

Simplify the expression:.

$\frac{x^{\frac{5}{6}}}{x^{\frac{7}{12}}}$

Possible Answers:

$\sqrt{x^4}$

$\sqrt{x^6}$

$\sqrt[4]{x}$

$\sqrt[6]{x}$

$\sqrt[6]{x^2}$

Correct answer:

$\sqrt[4]{x}$

Explanation:

Exponents in the denominator can be subtracted from exponents in the numerator.

$\small \frac{x^{\frac{5}{6}}}{x^{\frac{7}{12}}}=x^{\frac{5}{6}-\frac{7}{12}}=x^{\frac{10}{12}-\frac{7}{12}}=x^{\frac{3}{12}}=x^{\frac{1}{4}}$

Recall that $x^\frac{a}{b}=\sqrt[b]{x^a}$ .

Therefore, $x^\frac{1}{4}=\sqrt[4]{x}$ .

Report an Error

Example Question #2 : Using Radicals With Elementary Operations

Simplify:

$\sqrt{75}-\sqrt{27}$

Possible Answers:

$3\sqrt{5}$

$3\sqrt{2}$

$5\sqrt{3}$

$2\sqrt{3}$

$5\sqrt{2}$

Correct answer:

$2\sqrt{3}$

Explanation:

Try to group factors in pairs to get perfect squares under the square root:

$\sqrt{75}-\sqrt{27}= \sqrt{25\cdot 3}-\sqrt{9\cdot 3}=5\sqrt{3}-3\sqrt{3}=2\sqrt{3}$

Report an Error

View Tutors

Anne
Certified Tutor

University of Maryland-Baltimore, Doctor of Science, Accounting.

View Tutors

Satweka
Certified Tutor

The University of Texas at Dallas, Master of Science, Biomedical Engineering.

View Tutors

Tonja
Certified Tutor

McNeese State University, Bachelor in Arts, English.

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Algebra Tutors in Miami, Algebra Tutors in Los Angeles, Spanish Tutors in Washington DC, Statistics Tutors in San Diego, Math Tutors in San Francisco-Bay Area, French Tutors in San Diego, Statistics Tutors in San Francisco-Bay Area, SAT Tutors in New York City, SSAT Tutors in Miami, SAT Tutors in Philadelphia

Popular Courses & Classes

GMAT Courses & Classes in Philadelphia, ACT Courses & Classes in Seattle, GMAT Courses & Classes in Boston, MCAT Courses & Classes in New York City, ACT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Washington DC, ACT Courses & Classes in San Diego, ISEE Courses & Classes in Houston, ACT Courses & Classes in Philadelphia, Spanish Courses & Classes in Denver

Popular Test Prep

ISEE Test Prep in Miami, GRE Test Prep in Boston, GMAT Test Prep in Washington DC, GRE Test Prep in San Diego, GRE Test Prep in San Francisco-Bay Area, SAT Test Prep in San Diego, ACT Test Prep in Seattle, SSAT Test Prep in Atlanta, GRE Test Prep in Los Angeles, MCAT Test Prep in Atlanta

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

High School Math : Using Radicals with Elementary Operations

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #82 : Algebra Ii

Example Question #1 : Using Radicals With Elementary Operations

Example Question #2 : Using Radicals With Elementary Operations

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: