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 #41 : Solving Radical Equations

Solve the equation: $\sqrt{5x-4} +7 = 10$

Possible Answers:

$\frac{293}{5}$

$\textup{There is no solution.}$

$\frac{13}{5}$

$\frac{26}{5}$

Correct answer:

$\frac{13}{5}$

Explanation:

Subtract seven on both sides.

$\sqrt{5x-4} +7 -7= 10-7$

$\sqrt{5x-4} =3$

Square both sides. This will eliminate the radical on the left side.

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

5x-4 = 9

Add four on both sides.

5x-4 +4= 9+4

5x=13

Divide by five on both sides.

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

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

Report an Error

Example Question #4256 : Algebra Ii

Solve the equation: $3\sqrt[3]{4x-3} -3= 1$

Possible Answers:

$-\frac{17}{108}$

$\frac{43}{36}$

$\frac{919}{108}$

$\frac{41}{96}$

$\frac{145}{108}$

Correct answer:

$\frac{145}{108}$

Explanation:

Add three on both sides.

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

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

Divide by three on both sides.

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

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

Cube both sides to eliminate the radical. Simplify both sides.

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

$4x-3 = \frac{64}{27}$

Add three on both sides. This is the same as adding $\frac{81}{27}$ on the right side.

$4x-3+3=\frac{64}{27}+\frac{81}{27}$

$4x= \frac{145}{27}$

Divide by four on both sides. This is similar to multiplying one fourth on both sides and will isolate the x-variable on the left.

$4x\cdot \frac{1}{4}= \frac{145}{27}\cdot \frac{1}{4}$

$x=\frac{145}{108}$

The answer is: $\frac{145}{108}$

Report an Error

Example Question #43 : Solving And Graphing Radicals

Solve the equation: $\sqrt{6x-3}-28 = 30$

Possible Answers:

$\frac{1}{6}$

$\textup{There is no solution.}$

$\frac{3361}{6}$

$\frac{7}{6}$

$\frac{3367}{6}$

Correct answer:

$\frac{3367}{6}$

Explanation:

In order to solve this equation, first add 28 on both sides.

$\sqrt{6x-3}-28+28 = 30+28$

$\sqrt{6x-3}=58$

Square both sides.

$(\sqrt{6x-3})^2=58^2$

6x-3=3364

Add three on both sides.

6x-3+3=3364+3

6x=3367

Divide by six on both sides.

$\frac{6x}{6}=\frac{3367}{6}$

The answer is: $\frac{3367}{6}$

Report an Error

Example Question #41 : Solving Radical Equations

Solve the equation: $\sqrt[3]{6x-2}= 4$

Possible Answers:

$\textup{There is no solution.}$

$\frac{31}{3}$

Correct answer:

Explanation:

Cube both sides.

$(\sqrt[3]{6x-2})^3= 4^3$

This will eliminate the radical.

6x-2= 64

Add two on both sides.

6x-2+2= 64+2

6x=66

Divide by six on both sides.

$\frac{6x}{6}=\frac{66}{6}$

The answer is:

Report an Error

Example Question #45 : Solving And Graphing Radicals

Solve the equation: $\sqrt[5]{2x-6} = 2$

Possible Answers:

$\textup{There is no solution.}$

Correct answer:

Explanation:

Raise both sides of the equation by five.

$(\sqrt[5]{2x-6} )^5= 2^5$

2x-6 = 32

Add six on both sides.

2x-6 +6= 32+6

2x=38

Divide by two on both sides.

$\frac{2x}{2}=\frac{38}{2}$

Simplify both sides.

The answer is:

Report an Error

Example Question #46 : Solving And Graphing Radicals

Solve: $\sqrt{\frac{3}{2}x-1} = 5$

Possible Answers:

$36\sqrt{2}$

$24\sqrt{2}$

$\frac{26}{3}$

$\frac{52}{3}$

Correct answer:

$\frac{52}{3}$

Explanation:

Square both sides to eliminate the radical.

$(\sqrt{\frac{3}{2}x-1} )^2= 5^2$

The equation becomes:

$\frac{3}{2}x-1 = 25$

Add one on both sides.

$\frac{3}{2}x-1 +1= 25+1$

$\frac{3}{2}x = 26$

Multiply two-thirds on both sides to isolate the x-variable.

$\frac{3}{2}x \cdot \frac{2}{3}= 26\cdot \frac{2}{3}$

Simplify both sides.

The answer is: $\frac{52}{3}$

Report an Error

Example Question #47 : Solving And Graphing Radicals

Solve: $\frac{2}{\sqrt{2x}}+4=8$

Possible Answers:

$\frac{1}{4}$

$\textup{No solution.}$

$\frac{1}{16}$

$\frac{1}{8}$

$\frac{1}{64}$

Correct answer:

$\frac{1}{8}$

Explanation:

Subtract both sides by four.

$\frac{2}{\sqrt{2x}}+4-4=8-4$

$\frac{2}{\sqrt{2x}}=4$

Multiply by the denominator on both sides. The equation becomes:

$2=4\sqrt{2x}$

Divide by four on both sides to isolate the radical.

$\frac{2}{4}=\frac{4\sqrt{2x}}{4}$

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

Square both sides.

$\frac{1}{4} = 2x$

Divide by two on both sides.

The answer is: $\frac{1}{8}$

Report an Error

Example Question #48 : Solving And Graphing Radicals

Solve the radical equation: $\sqrt[5]{9x-3}+3 = 5$

Possible Answers:

$\frac{13}{9}$

$\frac{35}{9}$

$\frac{32765}{9}$

$-\frac{35}{9}$

$\frac{32771}{9}$

Correct answer:

$\frac{35}{9}$

Explanation:

Subtract three on both sides.

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

$\sqrt[5]{9x-3} = 2$

Take the fifth power of both sides to cancel the radical.

$(\sqrt[5]{9x-3})^5 = 2^5$

9x-3 = 32

Add three on both sides.

9x-3 +3= 32+3

9x=35

Divide by nine on both sides.

$\frac{9x}{9}=\frac{35}{9}$

The answer is: $\frac{35}{9}$

Report an Error

Example Question #49 : Solving And Graphing Radicals

Solve the radical equation: $\sqrt{3x-9} = 27$

Possible Answers:

240

$\textup{No solution.}$

246

$20\sqrt3$

Correct answer:

246

Explanation:

Square both sides to eliminate the radical.

$(\sqrt{3x-9} )^2= 27^{2}$

3x-9 = 729

Add 9 on both sides.

3x=738

Divide by three on both sides.

$\frac{3x}{3}=\frac{738}{3}$

The answer is: 246

Report an Error

Example Question #50 : Solving And Graphing Radicals

Solve the equation: $\sqrt{9x-2}-7 =1$

Possible Answers:

$\frac{11}{3}$

$\frac{22}{3}$

$\frac{33}{2}$

Correct answer:

$\frac{22}{3}$

Explanation:

Add 7 on both sides.

$\sqrt{9x-2}-7+7 =1+7$

$\sqrt{9x-2} =8$

Square both sides.

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

Simplify both sides of the equation.

9x-2 =64

Add 2 on both sides.

9x-2+2 =64+2

9x=66

Divide by nine on both sides.

$\frac{9x}{9}=\frac{66}{9}$

Reduce both fractions.

$x=\frac{66}{9}=\frac{3\times 11\times 2}{3\times 3} =\frac{22}{3}$

The answer is: $\frac{22}{3}$

Report an Error

View Algebra 2 Tutors

Satweka
Certified Tutor

The University of Texas at Dallas, Master of Science, Biomedical Engineering.

View Algebra 2 Tutors

Gabby
Certified Tutor

University of Oregon, Bachelor in Arts, Journalism. University of Oregon, Current Grad Student, Communication, General.

View Algebra 2 Tutors

Robert
Certified Tutor

Rensselaer Polytechnic Institute, Bachelors, Electrical Engineering. Brooklyn Polytechnic, Masters, Computer Science.

All Algebra II Resources

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

Popular Subjects

GRE Tutors in New York City, LSAT Tutors in San Francisco-Bay Area, English Tutors in Seattle, Reading Tutors in Dallas Fort Worth, Reading Tutors in Chicago, LSAT Tutors in Boston, Chemistry Tutors in Atlanta, ACT Tutors in New York City, SSAT Tutors in Washington DC, Computer Science Tutors in Denver

Popular Courses & Classes

LSAT Courses & Classes in Seattle, MCAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Boston, MCAT Courses & Classes in New York City, GMAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in New York City, ACT Courses & Classes in San Diego, SAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in San Diego, ACT Courses & Classes in Denver

Popular Test Prep

LSAT Test Prep in New York City, MCAT Test Prep in Philadelphia, ACT Test Prep in Houston, ISEE Test Prep in Dallas Fort Worth, MCAT Test Prep in Los Angeles, SSAT Test Prep in Chicago, GMAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Seattle, MCAT Test Prep in San Diego, ISEE 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

Algebra II : Solving and Graphing Radicals

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #41 : Solving Radical Equations

Example Question #4256 : Algebra Ii

Example Question #43 : Solving And Graphing Radicals

Example Question #41 : Solving Radical Equations

Example Question #45 : Solving And Graphing Radicals

Example Question #46 : Solving And Graphing Radicals

Example Question #47 : Solving And Graphing Radicals

Example Question #48 : Solving And Graphing Radicals

Example Question #49 : Solving And Graphing Radicals

Example Question #50 : 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: