We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Algebra II

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 #61 : Algebra Ii

Express the following exponent in radical form:

$r^2s^{\frac{1}{3}}y^{\frac{1}{2}}$

Possible Answers:

$r^2\sqrt[6]{s^2y^3}$

$r\sqrt[6]{s^2y^3}$

$r^6\sqrt[6]{s^2y^3}$

$r^4\sqrt[6]{s^2y^3}$

$r^3\sqrt[6]{s^2y^3}$

Correct answer:

$r^2\sqrt[6]{s^2y^3}$

Explanation:

Begin by converting each exponent to have a denominator of :

$r^2s^{\frac{1}{3}}y^{\frac{1}{2}}$

$=r^{\frac{12}{6}}s^{\frac{2}{6}}y^{\frac{3}{6}}$

Now, put this in radical form:

$=\sqrt[6]{r^{12}s^2y^3}$

Finally, simplify:

$=r^2\sqrt[6]{s^2y^3}$

Report an Error

Example Question #11 : Expressing Radicals As Exponents

Simplify the following radical expression using exponents. Express the final answer in radical form.

$\sqrt[6]{8n^9}$

Possible Answers:

$3n\sqrt{3n}$

$2n\sqrt{2n}$

$n\sqrt{2n}$

$2n\sqrt{3n}$

$n\sqrt{3n}$

Correct answer:

$n\sqrt{2n}$

Explanation:

Begin by converting the radical into exponent form:

$\sqrt[6]{8n^9}$

$(8^{\frac{1}{6}}n^{\frac{9}{6}})$

Simplify the exponent and multiply:

$(2^3^{\frac{1}{6}}n^{\frac{9}{6}})$

$(2^{\frac{1}{2}}n^{\frac{3}{2}})$

Convert into radical form:

$\sqrt{2n^3}$

Simplify:

$n\sqrt{2n}$

Report an Error

Example Question #11 : Expressing Radicals As Exponents

Express the following exponent in radical form:

$(3x)^{\frac{1}{2}}x^{\frac{1}{4}}$

Possible Answers:

$\sqrt[4]{9x^3}$

$\sqrt[4]{7x^3}$

$\sqrt[2]{9x^3}$

$\sqrt[2]{7x^3}$

$\sqrt[4]{9x^2}$

Correct answer:

$\sqrt[4]{9x^3}$

Explanation:

Begin by changing the fractional exponents so that they both have a common denominator of :

$(3x)^{\frac{1}{2}}x^{\frac{1}{4}}$

$=(3x)^{\frac{2}{4}}x^{\frac{1}{4}}$

Now, put this in radical form and simplify:

$=\sqrt[4]{(3x)^2x}$

$=\sqrt[4]{9x^2x}$

$=\sqrt[4]{9x^3}$

Report an Error

Example Question #1 : Simplifying Radicals

Factor and simplify the following radical expression:

$\sqrt[4]{81x^6y^5z^{10}}$

Possible Answers:

$3xyz\sqrt[4]{x^2yz^2}$

$3xyz^2\sqrt[4]{x^2y^2z^2}$

$3x^2yz^2\sqrt[4]{x^2yz^2}$

$3xyz^2\sqrt[4]{x^2yz^2}$

$3xy^2z^2\sqrt[4]{x^2yz^2}$

Correct answer:

$3xyz^2\sqrt[4]{x^2yz^2}$

Explanation:

Begin by factoring the integer:

$\sqrt[4]{81x^6y^5z^{10}}$

$\sqrt[4]{3^4x^6y^5z^{10}}$

$3\sqrt[4]{x^6y^5z^{10}}$

Now, simplify the exponents:

$3\sqrt[4]{x^4x^2y^4yz^{4}z^4z^2}$

$3xyzz\sqrt[4]{x^2yz^2}$

$3xyz^2\sqrt[4]{x^2yz^2}$

Report an Error

Example Question #2 : Simplifying Radicals

Factor and simplify the following radical expression:

$\sqrt[3]{(3n-2)^3}$

Possible Answers:

(3n-2)^3

3n+2

n-2

(3n-2)^2

3n-2

Correct answer:

3n-2

Explanation:

Begin by converting the radical into exponent form:

$\sqrt[3]{(3n-2)^3}$

$(3n-2)^3^{(\frac{1}{3})}$

Now, multiply the exponents:

3n-2

Report an Error

Example Question #3 : Simplifying Radicals

Factor and simplify the following radical expression:

$\sqrt[4]{18a^3bc^5}\cdot \sqrt[4]{27a^2b^6c}$

Possible Answers:

$3abc\sqrt[4]{6ab^3c^2}$

$3ab^2c\sqrt[4]{6ab^3c^2}$

$3a^2bc\sqrt[4]{6ab^3c^2}$

$3abc^2\sqrt[4]{6ab^3c^2}$

$3abc\sqrt[4]{6a^2b^3c^2}$

Correct answer:

$3abc\sqrt[4]{6ab^3c^2}$

Explanation:

Begin by converting the radical into exponent form:

$\sqrt[4]{18a^3bc^5}\cdot \sqrt[4]{27a^2b^6c}$

$(18a^3bc^5)^{\frac{1}{4}}\cdot ({27a^2b^6c})^{\frac{1}{4}}$

Now, combine the bases:

$(486a^5b^7c^6)^{\frac{1}{4}}$

Simplify the integer:

$(2\cdot 3\cdot 3^4a^5b^7c^6)^{\frac{1}{4}}$

Now, simplify the exponents:

$(2\cdot 3\cdot 3^4aa^4b^3b^4c^2c^4)^{\frac{1}{4}}$

Convert back into radical form and simplify:

$\sqrt[4]{2\cdot 3\cdot 3^4aa^4b^3b^4c^2c^4}$

$3abc\sqrt[4]{2\cdot 3ab^3c^2}$

$3abc\sqrt[4]{6ab^3c^2}$

Report an Error

Example Question #1 : Factoring Radicals

Factor and simplify the following radical expression:

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

Possible Answers:

$5\sqrt{3}-7$

$4\sqrt{3}-7$

$3\sqrt{3}-7$

$6\sqrt{3}-7$

$2\sqrt{3}-7$

Correct answer:

$4\sqrt{3}-7$

Explanation:

Begin by multiplying the numerator and denominator by the complement of the denominator:

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

Use the FOIL method to multiply the radicals. F (first) O (outer) I (inner) L (last)

$\frac{6\sqrt{3}-9-12+6\sqrt{3}}{12-6\sqrt{3}+6\sqrt{3}-9}$

Now, combine like terms:

$\frac{12\sqrt{3}-21}{3}$

Simplify:

$4\sqrt{3}-7$

Report an Error

Example Question #5 : Simplifying Radicals

Factor and simplify the following radical expression:

$\sqrt{\frac{1}{5}}-2\sqrt{20}+3\sqrt{5}$

Possible Answers:

$\frac{-4\sqrt{5}}{3}$

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

$\frac{4\sqrt{5}}{3}$

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

$\frac{-4\sqrt{3}}{5}$

Correct answer:

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

Explanation:

Begin by factoring the radicals:

$\sqrt{\frac{1}{5}}-2\sqrt{20}+3\sqrt{5}$

$\sqrt{\frac{1}{5}}-4\sqrt{5}+3\sqrt{5}$

Combine like terms:

$\sqrt{\frac{1}{5}}-\sqrt{5}$

Multiply the left side by $\frac{\sqrt{5}}{\sqrt{5}}$ and the right side by $\frac{5}{5}$

$\frac{1}{\sqrt{5}}-\sqrt{5}$

$\frac{1}{\sqrt{5}}\cdot \frac{\sqrt{5}}{\sqrt{5}}-\sqrt{5}\cdot\frac{5}{5}$

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

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

Report an Error

Example Question #6 : Simplifying Radicals

Factor and simplify the following radical expression:

$\sqrt[4]{24a^2b^3c^5}\cdot\sqrt[4]{48a^3b^3c^6}$

Possible Answers:

$2abc\sqrt[4]{72ab^2c^3}$

$2ab^2c^2\sqrt[4]{72ab^2c^3}$

$2abc^2\sqrt[4]{72ab^2c^3}$

$2a^2bc^2\sqrt[4]{72ab^2c^3}$

$2abc^2\sqrt[4]{72a^2b^2c^3}$

Correct answer:

$2abc^2\sqrt[4]{72ab^2c^3}$

Explanation:

Begin by converting the radicals into exponent form:

$\sqrt[4]{24a^2b^3c^5}\cdot\sqrt[4]{48a^3b^3c^6}$

$(24a^2b^3c^5)^{\frac{1}{4}}\cdot(48a^3b^3c^6)^{\frac{1}{4}}$

$(3\cdot 2^3a^2b^3c^5)^{\frac{1}{4}}\cdot(3\cdot 2^4a^3b^3c^6)^{\frac{1}{4}}$

Now, combine the bases:

$(3^2\cdot 2^7a^5b^6c^{11})^{\frac{1}{4}}$

$(3^2\cdot 2^7aa^4b^2b^4c^3c^{8})^{\frac{1}{4}}$

Convert back into radical form and simplify:

$\sqrt[4]{3^2\cdot 2^7aa^4b^2b^4c^3c^{8}}$

$2abc^2\sqrt[4]{3^22^3ab^2c^3}$

$2abc^2\sqrt[4]{72ab^2c^3}$

Report an Error

Example Question #2 : Factoring Radicals

Factor and simplify the following radical expression:

$\sqrt{3mn}+\sqrt{27m^3n}$

Possible Answers:

$(1+3m)\sqrt{3mn}$

$(1+m)\sqrt{3mn}$

$(1+2m)\sqrt{3mn}$

$(1+m)\sqrt{mn}$

$(1+2m)\sqrt{2mn}$

Correct answer:

$(1+3m)\sqrt{3mn}$

Explanation:

Begin by simplifying the right side of the rational expression:

$\sqrt{3mn}+\sqrt{27m^3n}$

$\sqrt{3mn}+3m\sqrt{3mn}$

$1\sqrt{3mn}+3m\sqrt{3mn}$

Now, combine like terms:

$(1+3m)\sqrt{3mn}$

Report an Error

View Tutors

Lydia
Certified Tutor

The Richard Stockton College of New Jersey, Bachelor of Science, Biochemistry and Molecular Biology.

View Tutors

Michelle
Certified Tutor

University of Nevada-Las Vegas, Bachelor of Science, Mathematics.

View Tutors

Kaylee
Certified Tutor

Brigham Young University, Bachelor, MFA - Animation.

All High School Math Resources

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

Popular Subjects

GRE Tutors in San Francisco-Bay Area, Reading Tutors in Los Angeles, SSAT Tutors in Philadelphia, Algebra Tutors in Dallas Fort Worth, Physics Tutors in San Francisco-Bay Area, Physics Tutors in Phoenix, LSAT Tutors in San Francisco-Bay Area, Computer Science Tutors in Phoenix, ACT Tutors in New York City, Biology Tutors in Washington DC

Popular Courses & Classes

ISEE Courses & Classes in Denver, SAT Courses & Classes in Atlanta, LSAT Courses & Classes in Washington DC, SAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Philadelphia, SSAT Courses & Classes in San Diego, SAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Denver, SAT Courses & Classes in Denver, MCAT Courses & Classes in Chicago

Popular Test Prep

LSAT Test Prep in Houston, ISEE Test Prep in Los Angeles, LSAT Test Prep in San Diego, SSAT Test Prep in Washington DC, GRE Test Prep in Denver, ACT Test Prep in Washington DC, ACT Test Prep in New York City, MCAT Test Prep in Chicago, GRE Test Prep in New York City, SSAT Test Prep in Miami

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 : Algebra II

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #61 : Algebra Ii

Example Question #11 : Expressing Radicals As Exponents

Example Question #11 : Expressing Radicals As Exponents

Example Question #1 : Simplifying Radicals

Example Question #2 : Simplifying Radicals

Example Question #3 : Simplifying Radicals

Example Question #1 : Factoring Radicals

Example Question #5 : Simplifying Radicals

Example Question #6 : Simplifying Radicals

Example Question #2 : Factoring Radicals

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: