Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Radicals and Fractions

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 #4211 : Algebra Ii

Rationalize: $\frac{9}{\sqrt{20}}$

Possible Answers:

$\frac{3\sqrt{2}}{4}$

$\frac{9\sqrt{2}}{4}$

$\frac{3\sqrt{5}}{10}$

$\frac{9\sqrt{5}}{10}$

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

Correct answer:

$\frac{9\sqrt{5}}{10}$

Explanation:

We can factor the square root twenty before rationalizing the value so that the final term would not be as difficult to factor.

Factor $\sqrt{20}$ using factors of perfect squares.

$\sqrt{20}= \sqrt{4}\times \sqrt5 = 2\sqrt5$

The expression becomes:

$\frac{9}{\sqrt{20}} = \frac{9}{2\sqrt{5}}$

Instead of multiplying $\sqrt{20}$ on both the top and bottom, we will multiply $\sqrt5$ on the top and bottom.

$\frac{9}{2\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{9\sqrt{5}}{10}$

The answer is: $\frac{9\sqrt{5}}{10}$

Report an Error

Example Question #222 : Simplifying Radicals

Try without a calculator.

Simplify:

$\sqrt{\frac{5}{8}}$

Possible Answers:

$\frac{\sqrt{10}}{2}$

$\frac{\sqrt{5}}{2}$

$\frac{\sqrt{10}}{4}$

None of the other choices gives the correct response.

$\frac{\sqrt{5}}{4}$

Correct answer:

$\frac{\sqrt{10}}{4}$

Explanation:

First, apply the Quotient of Radicals Property to split the radical into a numerator and a denominator:

$\sqrt{\frac{5}{8}}$

$= \frac{\sqrt{5}}{\sqrt{8}}$

Simplify the denominator by applying the Product of Radicals Property, as follows:

$= \frac{\sqrt{5}}{\sqrt{4} \cdot \sqrt{2}}$

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

Rationalize the denominator by multiplying both halves of the fraction by $\sqrt{2}$ :

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

Apply the Product of Radicals property in the numerator:

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

$= \frac{\sqrt{10}}{4}$ ,

the correct response.

Report an Error

Example Question #4212 : Algebra Ii

Try without a calculator.

Simplify:

$\sqrt{\frac{12}{7}}$

Possible Answers:

$\frac{3\sqrt{14} }{7}$

None of these

$\frac{ \sqrt{42} }{7}$

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

$\frac{6\sqrt{7} }{7}$

Correct answer:

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

Explanation:

First, apply the Quotient of Radicals Property to split the radical into a numerator and a denominator:

$\sqrt{\frac{12}{7}}$

$= \frac{\sqrt{12}}{\sqrt{7}}$

Simplify the numerator by applying the Product of Radicals Property, as follows:

$\frac{\sqrt{4 \cdot 3 }}{\sqrt{7}}$

$= \frac{\sqrt{4} \cdot \sqrt{3}}{\sqrt{7}}$

$= \frac{2 \sqrt{3}}{\sqrt{7}}$

Rationalize the denominator by multiplying both halves of the fraction by $\sqrt{7}$ :

$\frac{2 \sqrt{3} \cdot \sqrt{7} }{\sqrt{7} \cdot \sqrt{7}}$

Apply the Product of Radicals Property in the numerator:

$\frac{2 \sqrt{3 \cdot 7} }{7}$

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

Report an Error

View Algebra 2 Tutors

Scott
Certified Tutor

Boston University, Bachelor of Science, Film Studies.

View Algebra 2 Tutors

Shruti
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Premedicine.

View Algebra 2 Tutors

Chelsea
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Physics. The University of Texas at Dallas, Master of Science, Bioinf...

All Algebra II Resources

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

Popular Subjects

Calculus Tutors in Boston, Spanish Tutors in Chicago, Math Tutors in Philadelphia, Math Tutors in Dallas Fort Worth, Math Tutors in Boston, Calculus Tutors in Denver, Spanish Tutors in Denver, Chemistry Tutors in New York City, Algebra Tutors in Boston, Statistics Tutors in Chicago

Popular Courses & Classes

ISEE Courses & Classes in Phoenix, SAT Courses & Classes in Philadelphia, Spanish Courses & Classes in Atlanta, SSAT Courses & Classes in Philadelphia, GMAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in New York City, SAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Denver, LSAT Courses & Classes in Seattle, ISEE Courses & Classes in Philadelphia

Popular Test Prep

SSAT Test Prep in Dallas Fort Worth, GMAT Test Prep in Washington DC, GRE Test Prep in Houston, SAT Test Prep in San Diego, GRE Test Prep in San Diego, LSAT Test Prep in Phoenix, GRE Test Prep in Phoenix, SSAT Test Prep in San Diego, ISEE Test Prep in Seattle, LSAT Test Prep in Seattle

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 : Radicals and Fractions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #4211 : Algebra Ii

Example Question #222 : Simplifying Radicals

Example Question #4212 : Algebra Ii

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: