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 #95 : Solving Radical Equations

Solve the equation: $\sqrt{3x}-6= 11$

Possible Answers:

$\frac{23}{2}$

$\frac{34}{3}$

$\frac{289}{3}$

Correct answer:

$\frac{289}{3}$

Explanation:

Add six on both sides.

$\sqrt{3x}-6+6= 11+6$

$\sqrt{3x} = 17$

Square both sides to eliminate the radical.

$(\sqrt{3x}) ^2= 17^2$

3x=289

Divide both sides by three.

$\frac{3x}{3}=\frac{289}{3}$

The answer is: $\frac{289}{3}$

Report an Error

Example Question #96 : Solving Radical Equations

Solve the radical: $\sqrt{2-3x} = 40$

Possible Answers:

$-\frac{1598}{3}$

534

$-\frac{82}{3}$

$\textup{No solution.}$

Correct answer:

$-\frac{1598}{3}$

Explanation:

Square both sides of the equation to eliminate the radical.

$(\sqrt{2-3x})^2 = 40^2$

The equation becomes:

2-3x=1600

Subtract two from both sides.

2-3x-2=1600-2

-3x= 1598

Divide by negative three on both sides.

$\frac{-3x}{-3}=\frac{ 1598}{-3}$

The answer is: $-\frac{1598}{3}$

Report an Error

Example Question #411 : Radicals

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

Possible Answers:

$-\frac{1}{128}$

$\textup{No solution.}$

$-\frac{1}{2}$

$-\frac{1}{64}$

$-\frac{1}{4}$

Correct answer:

$-\frac{1}{128}$

Explanation:

Multiply by half on both sides.

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

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

Cube both sides to eliminate the radical.

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

$-2x = \frac{1}{64}$

Divide both sides by negative two. This is the same as multiplying by negative half on the right side.

$\frac{-2x}{-2} = \frac{1}{64}\cdot -\frac{1}{2}$

Reduce both fractions.

The answer is: $-\frac{1}{128}$

Report an Error

Example Question #412 : Radicals

Solve the radical equation: $\frac{x}{\sqrt{x-9}} = 6$

Possible Answers:

$\textup{No solution.}$

Correct answer:

Explanation:

Multiply both sides by the denominator to eliminate the fraction on the left side.

$\frac{x}{\sqrt{x-9}}\cdot \sqrt{x-9}= 6\cdot \sqrt{x-9}$

The equation becomes:

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

Square both sides to eliminate the radical.

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

x^2 = 36(x-9)

Distribute the 36 into the binomial.

x^2 = 36x-324

Subtract 36x and add 324 on both sides of the equation.

x^2 -[36x]+(324)= 36x-324-[36x]+(324)

The equation becomes a parabola, which can be factored.

x^2-36x+324 = 0

(x-18)^2 = 0

The value of x=18 . Check this value to see if substitution will satisfy the domain in the original equation.

$\frac{18}{\sqrt{18-9}}$ is valid since there is no negative in the radical, and there is not a zero denominator.

The answer is:

Report an Error

Example Question #99 : Solving Radical Equations

Solve the equation: $\sqrt{-9x} +5=9$

Possible Answers:

$-\frac{196}{9}$

$\textup{No solution.}$

$\frac{4}{3}$

$-\frac{16}{9}$

Correct answer:

$-\frac{16}{9}$

Explanation:

Subtract both sides by five.

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

$\sqrt{-9x} =4$

Square both sides.

$(\sqrt{-9x}) ^2=4^2$

-9x = 16

Divide by negative nine on both sides.

$\frac{-9x}{-9} = \frac{16}{-9}$

The answer is: $-\frac{16}{9}$

Report an Error

Example Question #1652 : Mathematical Relationships And Basic Graphs

Solve the radical equation: $2-\sqrt[3]{4x} = 1$

Possible Answers:

$\frac{1}{8}$

$\frac{3}{4}$

$\frac{1}{4}$

$\textup{No solution.}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{4}$

Explanation:

Add the radical on both sides.

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

The equation becomes:

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

Subtract 1 on both sides.

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

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

Cube both sides to eliminate the radical.

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

1=4x

Divide by four on both sides.

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

The answer is: $\frac{1}{4}$

Report an Error

Example Question #101 : Solving Radical Equations

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

Possible Answers:

$\textup{The answer is not given.}$

$\frac{9}{8}$

$\frac{9}{64}$

$\frac{81}{8}$

$\frac{81}{64}$

Correct answer:

$\frac{81}{64}$

Explanation:

Multiply the radical denominator on both sides.

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

The equation becomes:

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

Divide by two on both sides.

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

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

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

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

$\frac{81}{16}= 4x$

Divide by four on both sides. This is the same as multiplying one-fourth on both sides.

$\frac{81}{16}\cdot \frac{1}{4}= 4x\cdot \frac{1}{4}$

The answer is: $\frac{81}{64}$

Report an Error

Example Question #101 : Solving Radical Equations

Solve: $\frac{9\sqrt2}{\sqrt{2x}} = \sqrt2$

Possible Answers:

$\frac{9}{2}$

$\frac{3}{4}$

$\frac{81}{2}$

$\frac{2}{3}$

$\frac{81}{4}$

Correct answer:

$\frac{81}{2}$

Explanation:

Multiply the denominator on both sides to eliminate the denominator.

$\frac{9\sqrt2}{\sqrt{2x}} \cdot\sqrt{2x}= \sqrt2 \cdot\sqrt{2x}$

$9\sqrt2 = \sqrt{4x}$

Square both sides.

$(9\sqrt2)^2 =( \sqrt{4x})^2$

$81\cdot 2 = 4x$

Divide by four on both sides.

$\frac{81\cdot 2}{4} =\frac{ 4x}{4}$

The answer is: $\frac{81}{2}$

Report an Error

Example Question #4314 : Algebra Ii

Solve the equation: $\sqrt{5x-9} = 5$

Possible Answers:

$\frac{19}{25}$

$\frac{14}{5}$

$\frac{196}{5}$

$\frac{9}{5}$

$\frac{34}{5}$

Correct answer:

$\frac{34}{5}$

Explanation:

Square both sides of the radical to eliminate the square root.

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

The equation becomes:

5x-9 = 25

Add 9 on both sides.

5x-9 +9= 25+9

5x=34

Divide by 5 on both sides.

$\frac{5x}{5}=\frac{34}{5}$

The answer is: $\frac{34}{5}$

Report an Error

Example Question #4315 : Algebra Ii

Evaluate: $\frac{5\sqrt x}{\sqrt{9x}} = x$

Possible Answers:

$-\frac{5}{3}$

$\frac{5}{3}$

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

$\frac{3\sqrt5}{5}$

$\frac{1}{3}$

Correct answer:

$\frac{5}{3}$

Explanation:

Divide terms of the radicals on the left side.

$\frac{5\sqrt x}{\sqrt{9x}} = 5\sqrt{\frac{x}{9x}} = 5\sqrt{\frac{1}{9}}$

$x=5\sqrt{\frac{1}{9}} = 5\cdot \frac{1}{3} = \frac{5}{3}$

The answer is: $\frac{5}{3}$

Report an Error

View Algebra 2 Tutors

Daniel
Certified Tutor

Stony Brook University, Bachelors, Biology, General. SUNY College of Optometry, PHD, Optometry.

View Algebra 2 Tutors

Valsalakumari
Certified Tutor

Texas A & M University-Kingsville, Bachelors, Mathematics. Texas A & M University-Kingsville, Masters, Mathematics.

View Algebra 2 Tutors

Ruhhi
Certified Tutor

University of Delhi, Master's/Graduate, Physics.

All Algebra II Resources

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

Popular Subjects

SSAT Tutors in Los Angeles, Chemistry Tutors in Seattle, Chemistry Tutors in San Diego, Biology Tutors in Philadelphia, Math Tutors in Los Angeles, LSAT Tutors in Seattle, Reading Tutors in Philadelphia, Biology Tutors in Chicago, LSAT Tutors in San Diego, MCAT Tutors in Washington DC

Popular Courses & Classes

Spanish Courses & Classes in Boston, SSAT Courses & Classes in Chicago, GRE Courses & Classes in San Diego, GMAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Miami, ISEE Courses & Classes in Denver, LSAT Courses & Classes in Miami, MCAT Courses & Classes in Boston, Spanish Courses & Classes in Los Angeles, ISEE Courses & Classes in Atlanta

Popular Test Prep

ACT Test Prep in Boston, SAT Test Prep in Houston, ISEE Test Prep in Houston, LSAT Test Prep in New York City, GMAT Test Prep in Dallas Fort Worth, GRE Test Prep in San Diego, ACT Test Prep in Houston, GMAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Chicago, ISEE 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 #95 : Solving Radical Equations

Example Question #96 : Solving Radical Equations

Example Question #411 : Radicals

Example Question #412 : Radicals

Example Question #99 : Solving Radical Equations

Example Question #1652 : Mathematical Relationships And Basic Graphs

Example Question #101 : Solving Radical Equations

Example Question #101 : Solving Radical Equations

Example Question #4314 : Algebra Ii

Example Question #4315 : Algebra Ii

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: