We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Understanding Radicals

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Radicals

Simplify the expression. Find the positive solution only.

$\sqrt{50x^3y^4}$

Possible Answers:

25xy

$25x^2y^4\sqrt{2x}$

$5xy\sqrt{2x}$

$5xy^2\sqrt{2x}$

$xy^2\sqrt{50xy^2}$

Correct answer:

$5xy^2\sqrt{2x}$

Explanation:

When working in square roots, each component can be treated separately.

$\sqrt{50x^3y^4}=\sqrt{50}\sqrt{x^3}\sqrt{y^4}$

Now, we can simplify each term.

$\sqrt{50}=5\sqrt{2}$

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

$\sqrt{y^4}=y^2$

Combine the simplified terms to find the answer. Anything outside of the square root is combined, while anything under the root is combined under the root.

$(5\sqrt{2})(x\sqrt{x})(y^2)=5xy^2\sqrt{2x}$

Report an Error

Example Question #1 : Understanding Radicals

Convert the radical to exponential notation.

$\small \sqrt[4]{13}$

Possible Answers:

$\small 13^4$

$\small 169$

$\small \sqrt{13^4}$

$13^{\frac{1}{4}}$

Correct answer:

$13^{\frac{1}{4}}$

Explanation:

Remember that any term outside the radical will be in the denominator of the exponent.

$\sqrt[b]{x^a}=x^{\frac{a}{b}}$

Since does not have any roots, we are simply raising it to the one-fourth power.

$\sqrt[4]{13}=13^{\frac{1}{4}}$

Report an Error

Example Question #2 : Expressing Radicals As Exponents

What is the value of $9^ \frac{5}{2}$ ?

Possible Answers:

2.41

243

Correct answer:

243

Explanation:

An exponent written as a fraction can be rewritten using roots. $9^ \frac{5}{2}$ can be reqritten as $\sqrt[2]{9^5}$ . The bottom number on the fraction becomes the root, and the top becomes the exponent you raise the number to. $\sqrt[2]{9^5}$ is the same as $(\sqrt[2]{9})^{5}=3^{5}$ . This will give us the answer of 243.

Report an Error

Example Question #1 : Expressing Radicals As Exponents

Express the following radical in rational (exponential) form:

$\sqrt{8x^3y^4}$

Possible Answers:

$2^{(\frac{3}{2})}x^{(\frac{3}{2})}y^{(\frac{3}{2})}$

$2^2x^{(\frac{3}{2})}y^2$

$2^{(\frac{3}{2})}x^{(\frac{3}{2})}y^2$

2^2x^2y^2

$2^{(\frac{3}{2})}x^2y^2$

Correct answer:

$2^{(\frac{3}{2})}x^{(\frac{3}{2})}y^2$

Explanation:

To convert the radical to exponent form, begin by converting the integer:

$\sqrt{8x^3y^4}$

$=\sqrt{2^3x^3y^4}$

Now, divide each exponent by to clear the square root:

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

Finally, simplify the exponents:

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

Report an Error

Example Question #1 : Understanding Radicals

Express the following radical in rational (exponential) form:

$\sqrt[4]{96a^5b^7c^8}$

Possible Answers:

$3^{\frac{1}{4}}2^{\frac{5}{4}}a^{\frac{1}{4}}b^{\frac{7}{4}}c^2$

$3^{\frac{5}{4}}a^{\frac{5}{4}}b^{\frac{7}{4}}c^2$

$2^{\frac{5}{4}}a^{\frac{5}{4}}b^{\frac{7}{4}}c^2$

$3^{\frac{1}{4}}2^{\frac{5}{4}}a^{\frac{5}{4}}b^{\frac{7}{4}}c^2$

$3^{\frac{1}{4}}2^{\frac{5}{4}}a^{\frac{5}{4}}b^{\frac{7}{4}}$

Correct answer:

$3^{\frac{1}{4}}2^{\frac{5}{4}}a^{\frac{5}{4}}b^{\frac{7}{4}}c^2$

Explanation:

To convert the radical to exponent form, begin by converting the integer:

$\sqrt[4]{96a^5b^7c^8}$

$=\sqrt[4]{3\cdot 2^5a^5b^7c^8}$

Now, divide each exponent by to cancel the radical:

$=3^{\frac{1}{4}}2^{\frac{5}{4}}a^{\frac{5}{4}}b^{\frac{7}{4}}c^{\frac{8}{4}}$

Finally, simplify the exponents:

$=3^{\frac{1}{4}}2^{\frac{5}{4}}a^{\frac{5}{4}}b^{\frac{7}{4}}c^2$

Report an Error

Example Question #4 : Understanding Radicals

Which fraction is equivalent to $\frac{x^{\frac{5}{2}}}{x^{\frac{1}{2}}+y^{\frac{1}{2}}}$ ?

Possible Answers:

$\frac{x^3-x^{\frac{5}{2}}y^\frac{1}{2}}{x+y}$

$\frac{x^3+x^{\frac{5}{2}}y^\frac{1}{2}}{x-y}$

$\frac{x^3+x^{\frac{5}{2}}y^\frac{1}{2}}{x+y}$

$\frac{x^3-x^{\frac{5}{2}}y^\frac{1}{2}}{x-y}$

Correct answer:

$\frac{x^3-x^{\frac{5}{2}}y^\frac{1}{2}}{x-y}$

Explanation:

Multiply the numerator and denominator by the compliment of the denominator:

$=\frac{x^{\frac{5}{2}}}{x^{\frac{1}{2}}+y^{\frac{1}{2}}} \cdot \frac{x^{\frac{1}{2}}-y^{\frac{1}{2}}}{x^{\frac{1}{2}}-y^{\frac{1}{2}}}$

Simplify the expression:

$=\frac{x^3-x^{\frac{5}{2}}y^\frac{1}{2}}{x-y}$

Report an Error

Example Question #1 : Expressing Radicals As Exponents

Simplify the following radical. Express in rational (exponential) form.

$\frac{x^{\frac{2}{3}}}{x^{\frac{2}{3}}-x^{\frac{-1}{3}}}$

Possible Answers:

$\frac{x^2}{x-1}$

$\frac{x}{x-2}$

$\frac{x}{x^2-1}$

$\frac{x}{x-1}$

Correct answer:

$\frac{x}{x-1}$

Explanation:

Multiply the numerator and denominator by the compliment of the denominator:

$=\frac{x^{\frac{2}{3}}}{x^{\frac{2}{3}}-x^{\frac{-1}{3}}} \cdot \frac{x^{\frac{1}{3}}}{x^{\frac{1}{3}}}$

Simplify the expression:

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

Report an Error

Example Question #5 : Expressing Radicals As Exponents

Choose the fraction equivalent to $\frac{x^{\frac{1}{2}}-y^{\frac{1}{2}}}{x^{\frac{1}{2}}+y^{\frac{1}{2}}}$ .

Possible Answers:

$\frac{x+2x^{\frac{1}{2}}y^{\frac{1}{2}}+y}{x-y}$

$\frac{x-2x^{\frac{1}{2}}y^{\frac{1}{2}}+y}{x-y}$

$\frac{x+2x^{\frac{1}{2}}y^{\frac{1}{2}}+y}{x+y}$

$\frac{x-2x^{\frac{1}{2}}y^{\frac{1}{2}}+y}{x+y}$

Correct answer:

$\frac{x-2x^{\frac{1}{2}}y^{\frac{1}{2}}+y}{x-y}$

Explanation:

Multiply the numerator and denominator by the compliment of the denominator:

$=\frac{x^{\frac{1}{2}}-y^{\frac{1}{2}}}{x^{\frac{1}{2}}+y^{\frac{1}{2}}}$ $\cdot \frac{x^{\frac{1}{2}}-y^{\frac{1}{2}}}{x^{\frac{1}{2}}-y^{\frac{1}{2}}}$

Simplify the expression:

$=\frac{x-2x^{\frac{1}{2}}y^{\frac{1}{2}}+y}{x-y}$

Report an Error

Example Question #5 : Understanding Radicals

Simplify the following radical. Express in rational (exponential) form.

$(\frac{a^{\frac{-2}{3}}}{2^{\frac{1}{2}}a^2})^{\frac{-1}{2}}$

Possible Answers:

$2^{\frac{1}{3}}a^{\frac{4}{3}}$

$2^{\frac{1}{4}}a^{\frac{4}{3}}$

$2^{\frac{1}{4}}a^{\frac{5}{3}}$

$2^{\frac{1}{2}}a^{\frac{4}{3}}$

Correct answer:

$2^{\frac{1}{4}}a^{\frac{4}{3}}$

Explanation:

Multiply the numerator and denominator to the exponent:

$(\frac{a^{\frac{-2}{3}}}{2^{\frac{1}{2}}a^2})^{\frac{-1}{2}}$

$=\frac{a^{\frac{1}{3}}}{2^{\frac{-1}{4}}a^{-1}}$

Simplify the expression by combining like terms:

$=2^{\frac{1}{4}}a^{\frac{4}{3}}$

Report an Error

Example Question #3 : Expressing Radicals As Exponents

Express the following radical in rational (exponential) form:

$\sqrt[3]{16x^5y^6z^8}$

Possible Answers:

$2^{\frac{4}{3}}x^{\frac{5}{3}}y^{\frac{7}{3}}z^{\frac{8}{3}}$

$2^{\frac{4}{3}}x^{\frac{5}{3}}y^2z^{\frac{8}{3}}$

$2^{\frac{4}{3}}x^2y^2z^{\frac{8}{3}}$

$2^2x^{\frac{5}{3}}y^2z^{\frac{8}{3}}$

$2^{\frac{4}{3}}x^{\frac{5}{3}}y^2z^2$

Correct answer:

$2^{\frac{4}{3}}x^{\frac{5}{3}}y^2z^{\frac{8}{3}}$

Explanation:

To convert the radical to exponent form, begin by converting the integer:

$\sqrt[3]{16x^5y^6z^8}$

$=\sqrt[3]{2^4x^5y^6z^8}$

Now, divide each exponent by to remove the radical:

$=2^{\frac{4}{3}}x^{\frac{5}{3}}y^{\frac{6}{3}}z^{\frac{8}{3}}$

Finally, simplify the exponents:

$=2^{\frac{4}{3}}x^{\frac{5}{3}}y^2z^{\frac{8}{3}}$

Report an Error

View Tutors

Brooke
Certified Tutor

Tiffin University, Masters in Education, Education.

View Tutors

Diane
Certified Tutor

William Paterson University of New Jersey, Bachelor in Arts, Elementary School Teaching. University of Chicago, Master of Art...

View Tutors

MEER
Certified Tutor

IIT , Master's/Graduate, Microelectronics .

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

MCAT Tutors in San Francisco-Bay Area, MCAT Tutors in Phoenix, MCAT Tutors in Houston, Biology Tutors in Miami, Statistics Tutors in San Diego, GRE Tutors in San Francisco-Bay Area, French Tutors in Washington DC, Math Tutors in Atlanta, Physics Tutors in Boston, GMAT Tutors in Los Angeles

Popular Courses & Classes

LSAT Courses & Classes in Boston, ISEE Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in San Diego, ACT Courses & Classes in Philadelphia, GMAT Courses & Classes in Boston, ACT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Phoenix, GRE Courses & Classes in Houston, ISEE Courses & Classes in Chicago, MCAT Courses & Classes in Denver

Popular Test Prep

ISEE Test Prep in Houston, LSAT Test Prep in Chicago, SAT Test Prep in Los Angeles, GRE Test Prep in Houston, GMAT Test Prep in Boston, ISEE Test Prep in Chicago, MCAT Test Prep in San Francisco-Bay Area, ACT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Denver, SAT Test Prep in Chicago

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

High School Math : Understanding Radicals

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Radicals

Example Question #1 : Understanding Radicals

Example Question #2 : Expressing Radicals As Exponents

Example Question #1 : Expressing Radicals As Exponents

Example Question #1 : Understanding Radicals

Example Question #4 : Understanding Radicals

Example Question #1 : Expressing Radicals As Exponents

Example Question #5 : Expressing Radicals As Exponents

Example Question #5 : Understanding Radicals

Example Question #3 : Expressing Radicals As Exponents

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: