GRE Math : Simplifying Square Roots

Study concepts, example questions & explanations for GRE Math

Create An Account

All GRE Math Resources

13 Diagnostic Tests 452 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #792 : New Sat

Simplify $\sqrt{a^{3}b^{4}c^{5}}$ .

Possible Answers:

$a^{2}bc\sqrt{bc}$

$a^{2}b^{2}c^{2}\sqrt{bc}$

$a^{2}b^{2}c\sqrt{ab}$

$a^{2}bc^{2}\sqrt{ac}$

$ab^{2}c^{2}\sqrt{ac}$

Correct answer:

$ab^{2}c^{2}\sqrt{ac}$

Explanation:

Rewrite what is under the radical in terms of perfect squares:

$x^{2}=x\cdot x$

$x^{4}=x^{2}\cdot x^{2}$

$x^{6}=x^{3}\cdot x^{3}$

Therefore, $\sqrt{a^{3}b^{4}c^{5}}= \sqrt{a^{2}a^{1}b^{4}c^{4}c^{1}}=ab^{2}c^{2}\sqrt{ac}$ .

Report an Error

Example Question #2 : Properties Of Roots And Exponents

What is $\sqrt{50}$ ?

Possible Answers:

$10\sqrt{2}$

$5\sqrt{2}$

$2\sqrt{5}$

Correct answer:

$5\sqrt{2}$

Explanation:

We know that 25 is a factor of 50. The square root of 25 is 5. That leaves $\sqrt{2}$ which can not be simplified further.

Report an Error

Example Question #793 : New Sat

Which of the following is equivalent to $\frac{x + \sqrt{3}}{3x + \sqrt{2}}$ ?

Possible Answers:

$\frac{3x^{2} + 3x\sqrt{2} + x\sqrt{3} +\sqrt{6}}{9x^{2} - 2}$

$\frac{3x^{2} + \sqrt{6}}{3x - 2}$

$\frac{4x + \sqrt{5}}{3x + 2}$

$\frac{3x^{2} - \sqrt{6}}{9x^{2} + 2}$

$\frac{3x^{2} -x \sqrt{2} + 3x\sqrt{3} - \sqrt{6}}{9x^{2} - 2}$

Correct answer:

$\frac{3x^{2} -x \sqrt{2} + 3x\sqrt{3} - \sqrt{6}}{9x^{2} - 2}$

Explanation:

Multiply by the conjugate and the use the formula for the difference of two squares:

$\frac{x + \sqrt{3}}{3x + \sqrt{2}}$

$\frac{x + \sqrt{3}}{3x + \sqrt{2}}\cdot \frac{3x - \sqrt{2}}{3x - \sqrt{2}}$

$\frac{3x^{2} -x \sqrt{2} + 3x\sqrt{3} - \sqrt{6}}{(3x)^{2} - (\sqrt{2})^{2}}$

$\frac{3x^{2} -x \sqrt{2} + 3x\sqrt{3} - \sqrt{6}}{9x^{2} - 2}$

Report an Error

Example Question #1132 : Act Math

Which of the following is the most simplified form of:

$\sqrt{468}$

Possible Answers:

$17\sqrt{2}$

$\sqrt{468}$

$6\sqrt{13}$

$2\sqrt{117}$

$4\sqrt{29}$

Correct answer:

$6\sqrt{13}$

Explanation:

First find all of the prime factors of 468

$468=6\ast78=6\ast6\ast13=2\ast3\ast2\ast3\ast13$

So $\sqrt{468}=\sqrt{2\ast2\ast3\ast3\ast13}=2\ast3\sqrt{13}=6\sqrt{13}$

Report an Error

Example Question #1 : Simplifying Square Roots

What is $\sqrt{432}$ equal to?

Possible Answers:

$6\sqrt{3}$

$12\sqrt{3}$

$6\sqrt{4}$

$144\sqrt{3}$

$12\sqrt{12}$

Correct answer:

$12\sqrt{3}$

Explanation:

$\sqrt{432}$

1. We know that 432=(144)(3) , which we can separate under the square root:

$\sqrt{144\cdot 3}$

2. 144 can be taken out since it is a perfect square: $12\cdot12=144$ . This leaves us with:

$12\sqrt{3}$

This cannot be simplified any further.

Report an Error

All GRE Math Resources

13 Diagnostic Tests 452 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

MCAT Tutors in Dallas Fort Worth, GRE Tutors in Atlanta, GMAT Tutors in New York City, Physics Tutors in San Diego, Calculus Tutors in Miami, Biology Tutors in San Francisco-Bay Area, GMAT Tutors in Chicago, Biology Tutors in Washington DC, SAT Tutors in Houston, French Tutors in Denver

Popular Courses & Classes

SSAT Courses & Classes in Denver, MCAT Courses & Classes in Miami, GRE Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Philadelphia, GRE Courses & Classes in Boston, SAT Courses & Classes in Seattle, SSAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Miami, GRE Courses & Classes in Miami, LSAT Courses & Classes in Miami

Popular Test Prep

SAT Test Prep in Phoenix, LSAT Test Prep in Phoenix, SAT Test Prep in Boston, LSAT Test Prep in Atlanta, LSAT Test Prep in Miami, MCAT Test Prep in Seattle, LSAT Test Prep in New York City, GMAT Test Prep in Philadelphia, SSAT Test Prep in San Francisco-Bay Area, ACT 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)

Email address:
Your name:
Feedback:

GRE Math : Simplifying Square Roots

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #792 : New Sat

Example Question #2 : Properties Of Roots And Exponents

Example Question #793 : New Sat

Example Question #1132 : Act Math

Example Question #1 : Simplifying Square Roots

All GRE Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details