Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : 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 #8 : Non Square Radicals

Simplify: $-\sqrt{ 120}$

Possible Answers:

$-2\sqrt{30}$

$-6\sqrt{5}$

$\textup{No solution.}$

$-4\sqrt{15}$

$-2\sqrt{10}$

Correct answer:

$-2\sqrt{30}$

Explanation:

In order to simplify this radical, rewrite the radical using common factors.

$-\sqrt{ 120} = -\sqrt{2} \cdot \sqrt{2}\cdot \sqrt{5} \cdot \sqrt{6}$

Simplify the square roots.

$-2\cdot \sqrt{5} \cdot \sqrt{6}$

Multiply the terms inside the radical.

The answer is: $-2\sqrt{30}$

Report an Error

Example Question #9 : Non Square Radicals

Simplify: $\sqrt{30} \cdot \sqrt{15}$

Possible Answers:

$2\sqrt{15}$

$3\sqrt{10}$

$5\sqrt2$

$15\sqrt2$

$\textup{The radicals cannot be simplified any further.}$

Correct answer:

$15\sqrt2$

Explanation:

Break down the two radicals by their factors.

$\sqrt{30} \cdot \sqrt{15} = (\sqrt{3}\times\sqrt{2}\times \sqrt{5})\cdot(\sqrt{3}\times \sqrt{5})$

A square root of a number that is multiplied by itself is equal to the number inside the radical.

$\sqrt{3}\cdot \sqrt{3}=3$

$\sqrt{5}\cdot \sqrt{5}=5$

Simplify the terms in the parentheses.

$(\sqrt{3}\times\sqrt{2}\times \sqrt{5})\cdot(\sqrt{3}\times \sqrt{5}) = 3\times 5 \times \sqrt2$

The answer is: $15\sqrt2$

Report an Error

Example Question #4 : Non Square Radicals

Simplify, if possible: $3\sqrt{5}+6\sqrt{50}+ 9\sqrt{500}$

Possible Answers:

$30\sqrt5+93\sqrt2$

$\textup{The radical cannot be simplified any further.}$

$123\sqrt2$

$123\sqrt5$

$30\sqrt2+93\sqrt5$

Correct answer:

$30\sqrt2+93\sqrt5$

Explanation:

The first term is already simplified. The second and third term will need to be simplified.

Write the common factors of the second radical and simplify.

$6\sqrt{50} =6\sqrt{25\times 2} = 6\sqrt{25}\times \sqrt{2} = 6(5)\sqrt2 = 30\sqrt2$

Repeat the process for the third term.

$9\sqrt{500} = 9\sqrt{100\times 5} = 9\sqrt{100}\times \sqrt{5} = 9(10)\sqrt{5} = 90\sqrt5$

Rewrite the expression.

$3\sqrt{5}+6\sqrt{50}+ 9\sqrt{500}= 3\sqrt{5}+30\sqrt2+90\sqrt5$

Combine like-terms.

The answer is: $30\sqrt2+93\sqrt5$

Report an Error

Example Question #11 : Non Square Radicals

What is the value of $\sqrt{288}+\sqrt{48}$ ?

Possible Answers:

$12\sqrt3+4\sqrt2$

$12\sqrt2+4\sqrt3$

$12\sqrt2+3\sqrt2$

$16\sqrt6$

$16\sqrt5$

Correct answer:

$12\sqrt2+4\sqrt3$

Explanation:

Simplify the first term by using common factors of a perfect square.

$\sqrt{288} = \sqrt{144\times 2} = \sqrt{144} \cdot \sqrt{2} = 12\sqrt2$

Simplify the second term also by common factors.

$\sqrt{48} =\sqrt{4\cdot 4\cdot 3} =\sqrt{4}\cdot \sqrt{4}\cdot \sqrt{3} = 4\sqrt3$

Combine the terms.

$\sqrt{288}+\sqrt{48}=12\sqrt2+4\sqrt3$

The coefficients cannot be combined since these are unlike terms.

The answer is: $12\sqrt2+4\sqrt3$

Report an Error

Example Question #11 : Non Square Radicals

Simplify: $\frac{\sqrt{32}}{\sqrt{6}}$

Possible Answers:

$\frac{\sqrt3}{4}$

$\frac{\sqrt3}{3}$

$\frac{\sqrt3}{2}$

$\frac{4\sqrt3}{3}$

$\frac{2\sqrt3}{3}$

Correct answer:

$\frac{4\sqrt3}{3}$

Explanation:

To simplify this, multiply the top and bottom by the denominator.

$\frac{\sqrt{32}}{\sqrt{6}}\cdot\frac{\sqrt{6}}{\sqrt{6}} = \frac{4\sqrt2\cdot \sqrt6}{6} =\frac{4\sqrt{12}}{6} =\frac{4\cdot 2\sqrt{3}}{6}$

Reduce the fraction.

The answer is: $\frac{4\sqrt3}{3}$

Report an Error

Example Question #31 : Radicals

Simplify: $\sqrt{927}$

Possible Answers:

$9\sqrt{103}$

$9\sqrt{17}$

$12\sqrt{7}$

$3\sqrt{103}$

$103\sqrt{3}$

Correct answer:

$3\sqrt{103}$

Explanation:

To simplify radicals, we need to find perfect squares to factor out. In this case, it's .

$\sqrt{927}=\sqrt{9}*\sqrt{103}=3\sqrt{103}$ .

Report an Error

Example Question #32 : Radicals

Simplify: $\sqrt{1248}$

Possible Answers:

$32\sqrt{39}$

$78\sqrt{14}$

$12\sqrt{78}$

$4\sqrt{78}$

$16\sqrt{13}$

Correct answer:

$4\sqrt{78}$

Explanation:

To simplify radicals, we need to find perfect squares to factor out. In this case, it's .

$\sqrt{1248}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$

Report an Error

Example Question #33 : Radicals

Simplify: $\sqrt{x^7y^3}$

Possible Answers:

$x^3y\sqrt{xy}$

$xy^2\sqrt{x^3y}$

$xy^2\sqrt{x^3y^2}$

$x^3y\sqrt{x^3y}$

$x^6y\sqrt{xy}$

Correct answer:

$x^3y\sqrt{xy}$

Explanation:

To simplify radicals, we need to find perfect squares to factor out. In this case, it's (x^3)^2,y^2 .

$\sqrt{x^7y^3}=\sqrt{x^6}*\sqrt{y^2}*\sqrt{xy}=\sqrt{(x^3)^2}*y\sqrt{xy}=x^3y\sqrt{xy}$

Report an Error

Example Question #34 : Radicals

Simplify: $\sqrt{128x^4y^5}$

Possible Answers:

$64xy\sqrt{2xy}$

$8x^2y^2\sqrt{2y}$

$64xy\sqrt{2y}$

$8x^2y^2\sqrt{2x}$

$8x^2y^2\sqrt{2xy}$

Correct answer:

$8x^2y^2\sqrt{2y}$

Explanation:

To simplify radicals, we need to find perfect squares to factor out. In this case, it's 64,(x^2)^2, (y^2)^2 .

$\sqrt{128x^4y^5}=\sqrt{64}*\sqrt{(x^2)^2}*\sqrt{(y^2)^2}*\sqrt{2y}=8x^2y^2\sqrt{2y}$

Report an Error

Example Question #35 : Radicals

Simplify: $2\sqrt{60} \cdot 3\sqrt{10}$

Possible Answers:

120

$60\sqrt6$

$24\sqrt{150}$

180

$30\sqrt6$

Correct answer:

$60\sqrt6$

Explanation:

Multiply the radicals.

$\sqrt{60} \times \sqrt{10} = \sqrt{600}$

Simplify this by writing the factors using perfect squares.

$\sqrt{600} = \sqrt{100} \times \sqrt{6} = 10\sqrt6$

Multiply this with the integers.

$2\sqrt{60} \cdot 3\sqrt{10} = 2\cdot 3 \cdot 10\sqrt6 = 60\sqrt6$

The answer is: $60\sqrt6$

Report an Error

View Algebra 2 Tutors

Chelsea
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Physics. The University of Texas at Dallas, Master of Science, Bioinf...

View Algebra 2 Tutors

Rachel
Certified Tutor

Grand Canyon University, Bachelor of Science, Mathematics Teacher Education. Grand Canyon University, Master of Science, Addi...

View Algebra 2 Tutors

Samantha
Certified Tutor

Middlesex County College, Associate in Science, Sustainability Studies.

All Algebra II Resources

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

Popular Subjects

LSAT Tutors in New York City, Algebra Tutors in Miami, Math Tutors in Washington DC, Statistics Tutors in Washington DC, GRE Tutors in Phoenix, MCAT Tutors in Seattle, English Tutors in Philadelphia, MCAT Tutors in Denver, ISEE Tutors in Washington DC, SSAT Tutors in Los Angeles

Popular Courses & Classes

GRE Courses & Classes in Philadelphia, ISEE Courses & Classes in Atlanta, GRE Courses & Classes in Miami, GRE Courses & Classes in Los Angeles, GMAT Courses & Classes in Washington DC, SAT Courses & Classes in Washington DC, MCAT Courses & Classes in Los Angeles, Spanish Courses & Classes in Seattle, ISEE Courses & Classes in Boston, SSAT Courses & Classes in Boston

Popular Test Prep

SSAT Test Prep in San Francisco-Bay Area, GRE Test Prep in New York City, MCAT Test Prep in Dallas Fort Worth, ACT Test Prep in Washington DC, GMAT Test Prep in Miami, SAT Test Prep in San Diego, GRE Test Prep in Seattle, LSAT Test Prep in Atlanta, LSAT Test Prep in Philadelphia, LSAT Test Prep in San Diego

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 : Radicals

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #8 : Non Square Radicals

Example Question #9 : Non Square Radicals

Example Question #4 : Non Square Radicals

Example Question #11 : Non Square Radicals

Example Question #11 : Non Square Radicals

Example Question #31 : Radicals

Example Question #32 : Radicals

Example Question #33 : Radicals

Example Question #34 : Radicals

Example Question #35 : Radicals

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: