We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Algebra II

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 #11 : Radicals And Fractions

Simplify:

$\frac{10}{2\sqrt{5}}$

Possible Answers:

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

$\sqrt{10}$

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

$\sqrt{5}$

$\frac{5}{2}$

Correct answer:

$\sqrt{5}$

Explanation:

First, we can simplify the expression by dividing the integers on the top and bottom of the fraction.

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

In order to simplify this problem we need to multiply the top and bottom terms of the fraction by the radical in the denominator. This is because we always want an integer in the denominator.

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

Simplify.

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

Report an Error

Example Question #11 : Radicals And Fractions

Simplify:

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

Possible Answers:

$2+2\sqrt{2}$

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

$2-2\sqrt{2}$

$3-2\sqrt{2}$

$3+2\sqrt{2}$

Correct answer:

$3+2\sqrt{2}$

Explanation:

In order to get rid of the radical on the bottom of the fraction, we need to multiply the top and bottom of the fraction by the conjugate. The conjugate is the expression that possesses the opposite sign of the radical expression on the bottom of the fraction:

$\sqrt{2}-1\rightarrow\sqrt{2}+1$

Therefore:

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

Simplify.

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

Report an Error

Example Question #13 : Radicals And Fractions

Simplify:

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

Possible Answers:

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

$\sqrt{2}-1$

$\sqrt{2}+1$

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

Correct answer:

$\sqrt{2}-1$

Explanation:

$\sqrt{2}+1\rightarrow\sqrt{2}-1$

Therefore:

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

Simplify.

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

Report an Error

Example Question #281 : Radicals

Simplify:

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

Possible Answers:

$3\sqrt{3}-1$

$\sqrt{3}-1$

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

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

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

Correct answer:

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

Explanation:

$\sqrt{3}-1\rightarrow \sqrt{3}+1$

Therefore:

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

Simplify.

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

Report an Error

Example Question #22 : Radicals And Fractions

Simplify: $\frac{2-2\sqrt{2}}{\sqrt{6}}$

Possible Answers:

$\frac{2\sqrt{6}-4\sqrt{3}}{6}$

$\frac{\sqrt{6}-\sqrt{3}}{2}$

$\frac{2\sqrt{3}-\sqrt{6}}{3}$

$\frac{\sqrt{6}-2\sqrt{3}}{6}$

$\frac{\sqrt{6}-2\sqrt{3}}{3}$

Correct answer:

$\frac{\sqrt{6}-2\sqrt{3}}{3}$

Explanation:

In order to get rid of the radical on the bottom of the fraction, we need to multiply the top and bottom of the fraction by the conjugate. The conjugate is the expression that when multiplied to the denominator removes the radical:

$\frac{2-2\sqrt{2}}{\sqrt{6}}*\frac{\sqrt{6}}{\sqrt{6}}=\frac{2\sqrt{6}-2\sqrt{12}}{6}$

Simplify.

$\frac{2\sqrt{6}-2\sqrt{12}}{6}=\frac{2\sqrt{6}-4\sqrt{3}}{6}$

Now, factor out a .

$\frac{2\sqrt{6}-4\sqrt{3}}{6}=\frac{\sqrt{6}-2\sqrt{3}}{3}$

Report an Error

Example Question #23 : Radicals And Fractions

Simplify the expression: $\frac{1}{\sqrt2}+\frac{1}{\sqrt3}$

Possible Answers:

$6\sqrt{5}$

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

$\frac{3\sqrt{2}+2\sqrt{3}}{6}$

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

$\frac{\sqrt{30}}{6}$

Correct answer:

$\frac{3\sqrt{2}+2\sqrt{3}}{6}$

Explanation:

In order to simplify this, we will need to multiply both radicals together to obtain the least common denominator.

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

Convert both fractions so that they have similar common denominators.

$\frac{1}{\sqrt2}+\frac{1}{\sqrt3} = \frac{\sqrt3}{\sqrt6}+ \frac{\sqrt2}{\sqrt6}$

Combine the fractions. Do not add the terms of radicals on the numerator such that they would combine as a single radical!

$\sqrt{3}+\sqrt{2}\neq \sqrt{5}$

$\frac{\sqrt3+\sqrt2}{\sqrt6}$

Rationalize the denominator by multiplying $\frac{\sqrt{6}}{\sqrt6}$ .

$(\frac{\sqrt{6}}{\sqrt6})\frac{\sqrt3+\sqrt2}{\sqrt6} = \frac{\sqrt{18}+\sqrt{12}}{6}$

$\sqrt{18} = \sqrt{9}\cdot\sqrt{2} = 3\sqrt2$

$\sqrt{12} = \sqrt{4}\cdot \sqrt{3} = 2\sqrt{3}$

Replace the simplified radicals on the numerator.

The answer is: $\frac{3\sqrt{2}+2\sqrt{3}}{6}$

Report an Error

Example Question #4181 : Algebra Ii

Rationalize the denominator: $\frac{6}{\sqrt{30}}$

Possible Answers:

$\frac{2\sqrt{10}}{3}$

$\frac{\sqrt{30}}{3}$

$\sqrt{10}$

$\frac{\sqrt{30}}{6}$

$\frac{\sqrt{30}}{5}$

Correct answer:

$\frac{\sqrt{30}}{5}$

Explanation:

In order to eliminate the radical sign, multiply the top and the bottom by the denominator.

$\frac{6}{\sqrt{30}}\cdot \frac{\sqrt{30}}{\sqrt{30}} = \frac{6\sqrt{30}}{30}$

Reduce the numerator and denominator.

$\frac{6\sqrt{30}}{6\times 5}= \frac{\sqrt{30}}{5}$

The answer is: $\frac{\sqrt{30}}{5}$

Report an Error

Example Question #25 : Radicals And Fractions

Simplify:

$\sqrt{\frac{81x^2}{144y^6}}$

Possible Answers:

$\frac{3x}{12y^3}$

$\frac{9x}{12y^3}$

$\frac{9x}{11y^3}$

$\frac{9}{12y^3}$

$\frac{9x}{12y^2}$

Correct answer:

$\frac{9x}{12y^3}$

Explanation:

First, make the numerators and denominators separate radicals:

$\frac{\sqrt{81x^2}}{\sqrt{144y^6}}$ .

Then, simplify each one.

$\sqrt{81x^2}=9x$

and

$\sqrt{144y^6}=12y^3$ .

Then, put those together to get your answer of

$\frac{9x}{12y^3}$ .

Report an Error

Example Question #21 : Radicals And Fractions

Simplify the fraction: $\frac{2\sqrt{3}}{\sqrt{30}}$

Possible Answers:

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

$\frac{\sqrt{30}}{5}$

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

$\frac{\sqrt{6}}{5}$

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

Correct answer:

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

Explanation:

In order to simplify this fraction, we will need to rationalize the denominator.

Multiply the fraction by $\frac{\sqrt{30}}{\sqrt{30}}$ .

$\frac{2\sqrt{3}}{\sqrt{30}} \cdot \frac{\sqrt{30}}{\sqrt{30}} = \frac{2\sqrt{90}}{30} = \frac{2\sqrt{9}\cdot \sqrt{10}}{30}$

Simplify the fraction.

$\frac{2\sqrt{9}\cdot \sqrt{10}}{30} = \frac{2\cdot 3\cdot \sqrt{10}}{30} =\frac{\sqrt{10}}{5}$

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

Report an Error

Example Question #22 : Radicals And Fractions

$\sqrt{\frac{25x^4}{225y^{10}}}$

Possible Answers:

$\frac{x^2}{3y^2}$

$\frac{x^2}{y^2}$

$\frac{2x^2}{3y^2}$

$\frac{4x^2}{3y^2}$

$\frac{x^2}{3y}$

Correct answer:

$\frac{x^2}{3y^2}$

Explanation:

To simplify, first start by rewriting as:

$\frac{\sqrt{25x^4}}{\sqrt{225y^{10}}}$ .

Then, simplify the numerator and denominator separately.

$\sqrt{25x^4}=5x^2$

and

$\sqrt{225y^{10}}=15y^5$ .

Now, you have

$\frac{5x^2}{15y^5}$ .

Simplify to get

$\frac{x^2}{3y^2}$ .

Report an Error

View Algebra 2 Tutors

Samita
Certified Tutor

University of Houston, Bachelor of Science, Computer Science. University of Houston, Non Degree Bachelors, Biology, General.

View Algebra 2 Tutors

Laura
Certified Tutor

New York University, Bachelor in Arts, French.

View Algebra 2 Tutors

Soung
Certified Tutor

University of Chicago, Bachelor in Arts, Chemistry. Northwestern University, Doctor of Science, Molecular Pharmacology.

All Algebra II Resources

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

Popular Subjects

Computer Science Tutors in Chicago, SAT Tutors in Houston, Calculus Tutors in San Diego, ISEE Tutors in Dallas Fort Worth, GMAT Tutors in Seattle, Biology Tutors in San Diego, Reading Tutors in Los Angeles, Calculus Tutors in Seattle, French Tutors in Houston, SSAT Tutors in Seattle

Popular Courses & Classes

ACT Courses & Classes in Boston, LSAT Courses & Classes in New York City, GMAT Courses & Classes in Atlanta, MCAT Courses & Classes in Houston, ISEE Courses & Classes in Denver, ISEE Courses & Classes in Atlanta, Spanish Courses & Classes in Atlanta, SSAT Courses & Classes in Houston, LSAT Courses & Classes in Boston, LSAT Courses & Classes in Los Angeles

Popular Test Prep

SAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Denver, ACT Test Prep in Atlanta, ISEE Test Prep in San Francisco-Bay Area, SAT Test Prep in Miami, GMAT Test Prep in Atlanta, LSAT Test Prep in New York City, SAT Test Prep in Chicago, ISEE Test Prep in New York City, 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

Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #11 : Radicals And Fractions

Example Question #11 : Radicals And Fractions

Example Question #13 : Radicals And Fractions

Example Question #281 : Radicals

Example Question #22 : Radicals And Fractions

Example Question #23 : Radicals And Fractions

Example Question #4181 : Algebra Ii

Example Question #25 : Radicals And Fractions

Example Question #21 : Radicals And Fractions

Example Question #22 : Radicals And Fractions

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: