Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Solving and Graphing 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 #81 : Solving Radical Equations

Solve the equation: $\sqrt[3]{-6x-9} = 4$

Possible Answers:

$-\frac{7}{3}$

$-\frac{73}{3}$

$-\frac{13}{6}$

$-\frac{65}{6}$

$-\frac{73}{6}$

Correct answer:

$-\frac{73}{6}$

Explanation:

Raise both sides by the power of three in order to eliminate the radical.

$(\sqrt[3]{-6x-9} )^3= 4^3$

-6x-9 =64

Add nine on both sides.

-6x-9 +9=64+9

-6x =73

Divide by negative six on both sides.

$\frac{-6x}{-6} =\frac{73}{-6}$

The answer is: $-\frac{73}{6}$

Report an Error

Example Question #82 : Solving Radical Equations

Solve: $\sqrt[3]{3x-6} = \frac{1}{2}$

Possible Answers:

$-\frac{49}{24}$

$-\frac{35}{18}$

$-\frac{47}{24}$

$\frac{49}{24}$

$\frac{37}{18}$

Correct answer:

$\frac{49}{24}$

Explanation:

Cube both sides to eliminate the radical.

$(\sqrt[3]{3x-6} )^3= (\frac{1}{2})^3$

The equation becomes: $3x-6 = \frac{1}{8}$

Multiply by eight on both sides to eliminate the fraction.

$8(3x-6)= \frac{1}{8}\cdot 8$

24x-48=1

Add 48 on both sides.

24x-48+48=1+48

24x=49

Divide by 24 on both sides.

$\frac{24x}{24}=\frac{49}{24}$

The answer is: $\frac{49}{24}$

Report an Error

Example Question #83 : Solving And Graphing Radicals

Solve: $\sqrt{9x}+2 = 16$

Possible Answers:

$\frac{196}{9}$

$\frac{62}{3}$

$\frac{1}{7}$

$\frac{9}{49}$

Correct answer:

$\frac{196}{9}$

Explanation:

Subtract two from both sides.

$\sqrt{9x}+2 -2= 16-2$

$\sqrt{9x} = 14$

Square both sides in order to eliminate the radical.

$(\sqrt{9x}) ^2= 14^2$

9x=196

Divide by nine on both sides.

$\frac{9x}{9}=\frac{196}{9}$

The right side is irreducible.

The answer is: $\frac{196}{9}$

Report an Error

Example Question #81 : Solving Radical Equations

Solve the radical: $\sqrt{-5x+3} = 3$

Possible Answers:

$-\frac{5}{6}$

$-\frac{45}{4}$

$-\frac{1}{5}$

$-\frac{6}{5}$

Correct answer:

$-\frac{6}{5}$

Explanation:

Square both sides in order to eliminate the radical.

$(\sqrt{-5x+3} )^2= 3^2$

The equation becomes:

-5x+3=9

Subtract three from both sides.

-5x+3-3=9-3

-5x=6

Divide by negative five on both sides.

$\frac{-5x}{-5}=\frac{6}{-5}$

The answer is: $-\frac{6}{5}$

Report an Error

Example Question #85 : Solving And Graphing Radicals

Solve: $\sqrt[5]{-3x}-3 = -1$

Possible Answers:

$-\frac{32}{3}$

$-\frac{20}{3}$

$\textup{No solution.}$

$-\frac{2}{3}$

$-\frac{16}{3}$

Correct answer:

$-\frac{32}{3}$

Explanation:

Add three on both sides.

$\sqrt[5]{-3x}-3+3 = -1+3$

$\sqrt[5]{-3x} = 2$

Raise both sides by the power of five to eliminate the radical.

$(\sqrt[5]{-3x} )^5= 2^5$

-3x =32

Divide by negative three on both sides.

$\frac{-3x }{-3}=\frac{32}{-3}$

The answer is: $-\frac{32}{3}$

Report an Error

Example Question #86 : Solving And Graphing Radicals

Solve the equation: $\sqrt5 \cdot \sqrt{2x} -10= -9$

Possible Answers:

$\textup{No solution.}$

$\frac{1}{20}$

$\frac{1}{5}$

$\frac{1}{2}$

$\frac{1}{10}$

Correct answer:

$\frac{1}{10}$

Explanation:

The radicals can be combined as one radical by multiplying the two inner terms together.

The equation becomes:

$\sqrt{10x} -10= -9$

Add 10 on both sides.

$\sqrt{10x} -10+10= -9+10$

Simplify both sides.

$\sqrt{10x} =1$

Square both sides.

10x=1

Divide by ten on both sides.

$\frac{10x}{10}=\frac{1}{10}$

The answer is: $\frac{1}{10}$

Report an Error

Example Question #401 : Radicals

Solve the radical: $\sqrt{\sqrt{2x}} = \sqrt{8}$

Possible Answers:

256

128

Correct answer:

Explanation:

Rewrite the radicals so that they are in exponential form.

$\sqrt{x} = x^\frac{1}{2}$

$\sqrt{\sqrt{2x}} =[ (2x)^{\frac{1}{2}}]^{\frac{1}{2}} = (2x)^{\frac{1}{4}}$

The equation becomes:

$(2x)^{\frac{1}{4}} = 8^{\frac{1}{2}}$

Raise both sides by the power of four to eliminate the fractional exponents.

$[(2x)^{\frac{1}{4}}] ^4= [8^{\frac{1}{2}}]^4$

2x=64

Divide by two on both sides.

$\frac{2x}{2}=\frac{64}{2}$

The answer is:

Report an Error

Example Question #82 : Solving Radical Equations

Solve: $4=2^{10x-8}$

Possible Answers:

$-\frac{1}{2}$

$\frac{3}{4}$

Correct answer:

Explanation:

Evaluate by changing the base of the left term.

$2^2=2^{10x-8}$

Now that both bases are common, set the powers equal and solve for x.

2=10x-8

Add 8 on both sides.

2+8=10x-8+8

10=10x

Divide by ten on both sides.

$\frac{10}{10}=\frac{10x}{10}$

The answer is:

Report an Error

Example Question #81 : Solving And Graphing Radicals

Evaluate: $\sqrt[3]{2x-8} = 2$

Possible Answers:

$\textup{No solution.}$

-8,8

Correct answer:

Explanation:

Cube both sides to eliminate the radical.

$(\sqrt[3]{2x-8}) ^3= 2^3$

2x-8 =8

Add eight on both sides.

2x-8+(8) =8+(8)

2x=16

Divide by 2 on both sides.

$\frac{2x}{2}=\frac{16}{2}$

The answer is:

Report an Error

Example Question #81 : Solving Radical Equations

Solve: $2\sqrt[3]{2-5x} = 10$

Possible Answers:

$\frac{13}{5}$

$-\frac{123}{5}$

$\frac{123}{5}$

$-\frac{13}{5}$

$\frac{127}{5}$

Correct answer:

$-\frac{123}{5}$

Explanation:

Solve by first dividing both sides by two.

$\frac{2\sqrt[3]{2-5x} }{2}= \frac{10}{2}$

Simplify both sides.

$\sqrt[3]{2-5x} =5$

Cube both sides.

$(\sqrt[3]{2-5x})^3 =5^3$

2-5x =125

Subtract two from both sides.

2-5x -(2)=125-(2)

-5x=123

Divide by negative five on both sides.

$\frac{-5x}{-5}=\frac{123}{-5}$

The answer is: $-\frac{123}{5}$

Report an Error

View Algebra 2 Tutors

Shakeel
Certified Tutor

View Algebra 2 Tutors

Hayley
Certified Tutor

University of North Florida, Bachelor in Arts, English.

View Algebra 2 Tutors

Morgan
Certified Tutor

Catholic University of America, Bachelor of Science, International Finance.

All Algebra II Resources

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

Popular Subjects

SSAT Tutors in San Francisco-Bay Area, Biology Tutors in Boston, GRE Tutors in Boston, GRE Tutors in Philadelphia, English Tutors in Dallas Fort Worth, Biology Tutors in San Francisco-Bay Area, Spanish Tutors in Washington DC, English Tutors in Los Angeles, Computer Science Tutors in Los Angeles, Calculus Tutors in Houston

Popular Courses & Classes

SSAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Seattle, Spanish Courses & Classes in Atlanta, LSAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Boston, ACT Courses & Classes in Denver, MCAT Courses & Classes in Denver, LSAT Courses & Classes in Seattle, LSAT Courses & Classes in Miami, ACT Courses & Classes in New York City

Popular Test Prep

ACT Test Prep in New York City, MCAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Washington DC, SSAT Test Prep in Seattle, ISEE Test Prep in New York City, SAT Test Prep in Miami, MCAT Test Prep in Dallas Fort Worth, ACT Test Prep in San Francisco-Bay Area, ACT Test Prep in Dallas Fort Worth, MCAT Test Prep in Los Angeles

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 : Solving and Graphing Radicals

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #81 : Solving Radical Equations

Example Question #82 : Solving Radical Equations

Example Question #83 : Solving And Graphing Radicals

Example Question #81 : Solving Radical Equations

Example Question #85 : Solving And Graphing Radicals

Example Question #86 : Solving And Graphing Radicals

Example Question #401 : Radicals

Example Question #82 : Solving Radical Equations

Example Question #81 : Solving And Graphing Radicals

Example Question #81 : Solving Radical Equations

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: