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 #71 : Solving Radical Equations

Solve the equation: $\sqrt[3]{3x} = \frac{2}{3}$

Possible Answers:

$\frac{8}{81}$

$\frac{16}{81}$

$\frac{1}{3}$

$\frac{8}{9}$

$\frac{2}{27}$

Correct answer:

$\frac{8}{81}$

Explanation:

Cube both sides of the equation.

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

This will eliminate the radical on the left side.

$3x= (\frac{2}{3})(\frac{2}{3})(\frac{2}{3})$

$3x= \frac{8}{27}$

Divide by three on both sides. This is similar to multiplying one-third on both sides.

$3x \times \frac{1}{3}= \frac{8}{27} \times \frac{1}{3}=\frac{8}{81}$

The answer is: $\frac{8}{81}$

Report an Error

Example Question #72 : Solving And Graphing Radicals

Solve the radical equation: $3-\sqrt[3]{2-x} = -1$

Possible Answers:

$\textup{No solution.}$

Correct answer:

Explanation:

Subtract both sides by three.

$3-\sqrt[3]{2-x} -3= -1-3$

The equation becomes:

$-\sqrt[3]{2-x} =-4$

Divide both sides by negative one.

$\frac{-\sqrt[3]{2-x} }{-1}=\frac{-4}{-1}$

$\sqrt[3]{2-x} =4$

Cube both sides to eliminate the radical.

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

2-x = 64

Add on both sides.

2-x +x= 64+x

2= 64+x

Subtract 64 on both sides.

2-64= 64+x-64

The answer is:

Report an Error

Example Question #73 : Solving And Graphing Radicals

Solve the radical equation: $\sqrt[8]{2x-1} =2$

Possible Answers:

$\frac{255}{2}$

$\frac{63}{2}$

$\frac{17}{2}$

$\frac{65}{2}$

$\frac{257}{2}$

Correct answer:

$\frac{257}{2}$

Explanation:

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

$(\sqrt[8]{2x-1} )^8=2^8$

Simplify both sides.

2x-1=256

Add one on both sides.

2x-1+1=256+1

2x=257

Divide by two on both sides.

$\frac{2x}{2}=\frac{257}{2}$

The answer is: $\frac{257}{2}$

Report an Error

Example Question #74 : Solving And Graphing Radicals

Solve: $\frac{1}{\sqrt{3x}} = 4$

Possible Answers:

$\frac{1}{24}$

$\frac{1}{72}$

$\frac{1}{48}$

$\frac{16}{3}$

Correct answer:

$\frac{1}{48}$

Explanation:

Multiply by $\sqrt{3x}$ on both sides.

$\frac{1}{\sqrt{3x}} \cdot \sqrt{3x}= 4 \cdot \sqrt{3x}$

$1=4\sqrt{3x}$

Divide by 4 on both sides.

$\frac{1}{4}=\frac{4\sqrt{3x}}{4}$

$\frac{1}{4} =\sqrt{3x}$

Square both sides to eliminate the radical.

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

$\frac{1}{16} = 3x$

Divide by three on both sides. This is similar to multiplying both sides by one third.

$\frac{1}{16} \cdot \frac{1}{3}= 3x\cdot \frac{1}{3}$

The answer is: $\frac{1}{48}$

Report an Error

Example Question #75 : Solving And Graphing Radicals

Solve: $\frac{2}{\sqrt{8x}} = \sqrt{x}$

Possible Answers:

$\frac{\sqrt2}{2}$

$\textup{No solution.}$

$\frac{3\sqrt2}{4}$

$\frac{\sqrt5}{8}$

$\frac{\sqrt2}{4}$

Correct answer:

$\frac{\sqrt2}{2}$

Explanation:

Multiply both sides by the denominator on the left side.

$\frac{2}{\sqrt{8x}}\cdot \sqrt{8x} = \sqrt{x}\cdot \sqrt{8x}$

The equation becomes: $2 = \sqrt{8x^2}$

Square both sides to eliminate the radical.

$2 ^2= (\sqrt{8x^2})^2$

4=8x^2

Divide both sides by eight.

$\frac{4}{8}=\frac{8x^2}{8}$

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

Notice that the negative radical solution will not satisfy the original equation.

Rationalize the positive term.

$\frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt2}{2}$

The answer is: $\frac{\sqrt2}{2}$

Report an Error

Example Question #76 : Solving And Graphing Radicals

Solve: $\sqrt[4]{32x+1} = 3$

Possible Answers:

$\frac{145}{32}$

$\frac{7}{2}$

$\frac{4}{3}$

$\frac{41}{16}$

$\frac{5}{2}$

Correct answer:

$\frac{5}{2}$

Explanation:

Raise both sides to the power of four.

$(\sqrt[4]{32x+1}) ^4= 3^4$

Simplify both sides.

32x+1 = 81

Subtract 1 from both sides.

32x+1 -1= 81-1

32x=80

Divide by 32 on both sides.

$\frac{32x}{32}=\frac{80}{32}$

Reduce this fraction.

$\frac{80}{32} = \frac{16\times 5}{16\times 2}$

The answer is: $\frac{5}{2}$

Report an Error

Example Question #4291 : Algebra Ii

Solve the equation: $\sqrt[3]{8x-2} = 10$

Possible Answers:

128

125

$\frac{501}{4}$

$\frac{251}{4}$

Correct answer:

$\frac{501}{4}$

Explanation:

In order to eliminate the radical on both sides, we will need to cube both sides.

$(\sqrt[3]{8x-2})^3 = 10^3$

Simplify both sides.

8x-2 = 1000

Add two on both sides.

8x-2+2 = 1000+2

8x=1002

Divide by eight on both sides.

$\frac{8x}{8}=\frac{1002}{8}$

Reduce the fractions on both sides.

The answer is: $\frac{501}{4}$

Report an Error

Example Question #78 : Solving And Graphing Radicals

Solve: $\sqrt{-5x+3} = 4$

Possible Answers:

$\textup{No solution.}$

$-\frac{13}{5}$

$-\frac{26}{5}$

Correct answer:

$-\frac{13}{5}$

Explanation:

Square both sides to eliminate the radical.

$(\sqrt{-5x+3} )^2= 4^2$

-5x+3 = 16

Subtract three on both sides.

-5x+3 -3= 16-3

The equation becomes:

-5x= 13

Divide by negative five on both sides.

$\frac{-5x}{-5}= \frac{13}{-5}$

The answer is: $-\frac{13}{5}$

Report an Error

Example Question #79 : Solving And Graphing Radicals

Solve the equation: $\sqrt[4]{-3x}+8 = 11$

Possible Answers:

$\textup{No solution.}$

Correct answer:

Explanation:

Subtract eight from both sides.

$\sqrt[4]{-3x}+8-8 = 11-8$

$\sqrt[4]{-3x} =3$

Raise both sides by the power of four.

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

-3x =81

Divide both sides by three.

$\frac{-3x }{-3}=\frac{81}{-3}$

The answer is:

Report an Error

Example Question #80 : Solving And Graphing Radicals

Solve: $\sqrt{6x-9} -3 =5$

Possible Answers:

$\frac{73}{6}$

$\frac{53}{3}$

$\frac{13}{3}$

$\frac{13}{6}$

$\frac{53}{6}$

Correct answer:

$\frac{73}{6}$

Explanation:

Add three on both sides.

$\sqrt{6x-9} -3 +3=5+3$

$\sqrt{6x-9} = 8$

Square both sides.

$(\sqrt{6x-9})^2 = 8^2$

6x-9 = 64

Add nine on both sides.

6x-9+9 = 64+9

Simplify both sides.

6x=73

Divide by 6 on both sides.

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

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

Report an Error

View Algebra 2 Tutors

Sana
Certified Tutor

Loyola University-Chicago, Bachelor of Science, Psychology.

View Algebra 2 Tutors

Bagher
Certified Tutor

San Jose State University, Master's/Graduate, Physics.

View Algebra 2 Tutors

Alejandro
Certified Tutor

Kennesaw State University, Bachelor of Science, Computer Software Engineering.

All Algebra II Resources

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

Popular Subjects

Chemistry Tutors in Chicago, ISEE Tutors in Denver, English Tutors in New York City, Computer Science Tutors in New York City, Computer Science Tutors in San Francisco-Bay Area, Computer Science Tutors in Dallas Fort Worth, English Tutors in Washington DC, Reading Tutors in Denver, MCAT Tutors in Seattle, Spanish Tutors in Phoenix

Popular Courses & Classes

SSAT Courses & Classes in Chicago, SAT Courses & Classes in Philadelphia, Spanish Courses & Classes in Phoenix, Spanish Courses & Classes in San Diego, Spanish Courses & Classes in Miami, Spanish Courses & Classes in Seattle, GMAT Courses & Classes in San Diego, SAT Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Miami

Popular Test Prep

SAT Test Prep in Boston, ACT Test Prep in Los Angeles, LSAT Test Prep in San Diego, ISEE Test Prep in Miami, SAT Test Prep in Chicago, LSAT Test Prep in New York City, LSAT Test Prep in Dallas Fort Worth, SAT Test Prep in Seattle, ISEE Test Prep in San Diego, SAT 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 #71 : Solving Radical Equations

Example Question #72 : Solving And Graphing Radicals

Example Question #73 : Solving And Graphing Radicals

Example Question #74 : Solving And Graphing Radicals

Example Question #75 : Solving And Graphing Radicals

Example Question #76 : Solving And Graphing Radicals

Example Question #4291 : Algebra Ii

Example Question #78 : Solving And Graphing Radicals

Example Question #79 : Solving And Graphing Radicals

Example Question #80 : Solving And Graphing Radicals

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: