We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : High School Math

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 #11 : Factoring Radicals

Simplify the following radical expression:

$\sqrt{72a^5b^7c^6}$

Possible Answers:

$6a^2bc^3\sqrt{2ab}$

$6a^2b^3c\sqrt{2ab}$

$6ab^3c^3\sqrt{2ab}$

$6a^2b^3c^3\sqrt{2ab}$

$6a^2b^3c^3\sqrt{ab}$

Correct answer:

$6a^2b^3c^3\sqrt{2ab}$

Explanation:

Begin by factoring the integer:

$\sqrt{72a^5b^7c^6}$

$\sqrt{2^33^2a^5b^7c^6}$

Factor the exponents:

$6a^2b^3c^3\sqrt{2ab}$

Report an Error

Example Question #25 : Radicals

Simplify the following radical expression:

$\sqrt[3]{-40n^7m^4}$

Possible Answers:

$n^2m\sqrt[3]{5nm}$

$2n^2m\sqrt[3]{5nm}$

$-n^2m\sqrt[3]{5nm}$

$-2n^2m\sqrt[3]{5nm}$

$-2n^2m\sqrt[3]{6nm}$

Correct answer:

$-2n^2m\sqrt[3]{5nm}$

Explanation:

Begin by factoring the integer:

$\sqrt[3]{-40n^7m^4}$

$\sqrt[3]{-2^35n^7m^4}$

Factor the exponents:

$-2n^2m\sqrt[3]{5nm^}$

Report an Error

Example Question #1271 : High School Math

Simplify the following radical expression:

$\sqrt{n^2-10n+25}$

Possible Answers:

n-5

n-10

n-12

n-8

n-6

Correct answer:

n-5

Explanation:

Begin by factoring the expression:

$\sqrt{n^2-10n+25}$

$\sqrt{(n-5)^2}$

Now, take the square root:

n-5

Report an Error

Example Question #31 : Radicals

Simplify the following radical expression:

$\sqrt[3]{(3x-y)^5}$

Possible Answers:

$(3x-y)\sqrt[3]{(3x-y)^2}$

$(3x-y)^2\sqrt[3]{(3x-y)^3}$

$(3x-y)\sqrt[3]{(3x-y)^3}$

$(3x-y)\sqrt[3]{(3x-y)}$

$(3x-y)^2\sqrt[3]{(3x-y)^2}$

Correct answer:

$(3x-y)\sqrt[3]{(3x-y)^2}$

Explanation:

Simplify the radical expression:

$\sqrt[3]{(3x-y)^5}$

$\sqrt[3]{(3x-y)^2(3x-y)^3}$

$(3x-y)\sqrt[3]{(3x-y)^2}$

Report an Error

Example Question #1 : Factoring Radicals

Simplify the expression:

$\frac{3\sqrt[4]{32}}{2\sqrt[4]{162}}$

Possible Answers:

. $\frac{3\sqrt[4]{16}}{2\sqrt[4]{81}}$

$6\sqrt[4]{2}$

$\frac{2}{3}$

$\frac{3}{2}$

Correct answer:

Explanation:

Use the multiplication property of radicals to split the fourth roots as follows:

$\rightarrow \frac{3\sqrt[4]{16}\sqrt[4]{2}}{2\sqrt[4]{81}\sqrt[4]{2}}$

Simplify the new roots:

$\rightarrow \frac{3(2)\sqrt[4]{2}}{2(3)\sqrt[4]{2}}$

$\rightarrow \frac{6\sqrt[4]{2}}{6\sqrt[4]{2}}$

$\rightarrow 1$

Report an Error

Example Question #1272 : High School Math

Find the value of $\sqrt{80} + \sqrt{20}$ .

Possible Answers:

$\sqrt5$

$6\sqrt{10}$

$4\sqrt5$

$6\sqrt5$

Correct answer:

$6\sqrt5$

Explanation:

To solve this equation, we have to factor our radicals. We do this by finding numbers that multiply to give us the number within the radical.

$\sqrt{80} = \sqrt{20}\sqrt{4}$

$\sqrt{20} = \sqrt{5}\sqrt{4}$

Add them together:

$\sqrt5\sqrt4\sqrt4 + \sqrt5\sqrt4$

4 is a perfect square, so we can find the root:

$(2)(2)\sqrt5 + 2\sqrt5$

$4\sqrt5 + 2\sqrt5 = 6\sqrt5$

Since both have the same radical, we can combine them:

$4\sqrt5 + 2\sqrt5 = 6\sqrt5$

Report an Error

Example Question #12 : Simplifying Radicals

Factor and simplify the following radical expression:

$(4-2\sqrt{2})(\sqrt{2}-4)$

Possible Answers:

$10\sqrt{2}-20$

$12\sqrt{2}-16$

$12\sqrt{2}-20$

$12\sqrt{2}-18$

$14\sqrt{2}-20$

Correct answer:

$12\sqrt{2}-20$

Explanation:

Begin by using the FOIL method (First Outer Inner Last) to expand the expression.

$(4-2\sqrt{2})(\sqrt{2}-4)$

$4\sqrt{2}-16-4+8\sqrt{2}$

Now, combine like terms:

$12\sqrt{2}-20$

Report an Error

Example Question #82 : Algebra Ii

What is the value of $5\sqrt5 + 3 - 4\sqrt{2} +9 - 3\sqrt{5}$ ?

Possible Answers:

$2\sqrt{5} - 4\sqrt{2} + 12$

$2\sqrt{7} - 4\sqrt{7} + 12$

$4\sqrt{7} - 12$

$-2\sqrt{3} + 12$

$2\sqrt{10} - 4\sqrt{2} + 12$

Correct answer:

$2\sqrt{5} - 4\sqrt{2} + 12$

Explanation:

When combining terms involving radicals, we can only combine the ones that have the same radical. For this problem, that means $4\sqrt2$ has to stay on its own while we can combine $5\sqrt5$ and $-3\sqrt5$ into $2\sqrt5$ . The simple integers can be combined too, giving us our answer with three seperate terms.

Report an Error

Example Question #1273 : High School Math

Simplify the expression:.

$\frac{x^{\frac{5}{6}}}{x^{\frac{7}{12}}}$

Possible Answers:

$\sqrt[4]{x}$

$\sqrt[6]{x}$

$\sqrt{x^6}$

$\sqrt{x^4}$

$\sqrt[6]{x^2}$

Correct answer:

$\sqrt[4]{x}$

Explanation:

Exponents in the denominator can be subtracted from exponents in the numerator.

$\small \frac{x^{\frac{5}{6}}}{x^{\frac{7}{12}}}=x^{\frac{5}{6}-\frac{7}{12}}=x^{\frac{10}{12}-\frac{7}{12}}=x^{\frac{3}{12}}=x^{\frac{1}{4}}$

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

Therefore, $x^\frac{1}{4}=\sqrt[4]{x}$ .

Report an Error

Example Question #1274 : High School Math

Simplify:

$\sqrt{75}-\sqrt{27}$

Possible Answers:

$2\sqrt{3}$

$5\sqrt{3}$

$3\sqrt{2}$

$5\sqrt{2}$

$3\sqrt{5}$

Correct answer:

$2\sqrt{3}$

Explanation:

Try to group factors in pairs to get perfect squares under the square root:

$\sqrt{75}-\sqrt{27}= \sqrt{25\cdot 3}-\sqrt{9\cdot 3}=5\sqrt{3}-3\sqrt{3}=2\sqrt{3}$

Report an Error

View Tutors

Annalise
Certified Tutor

University of New Hampshire at Manchester, Master of Arts, Peace and Conflict Resolution Studies.

View Tutors

Melissa
Certified Tutor

Lock Haven University, Bachelor of Science, Accounting.

View Tutors

Matthew
Certified Tutor

Bluffton University, Bachelor of Education, Mathematics. Bluffton University, Masters in Education, Education.

All High School Math Resources

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

Popular Subjects

SAT Tutors in Washington DC, English Tutors in Phoenix, ACT Tutors in Miami, French Tutors in San Diego, French Tutors in Washington DC, Physics Tutors in Atlanta, Spanish Tutors in Washington DC, Computer Science Tutors in Washington DC, Computer Science Tutors in Seattle, SSAT Tutors in Chicago

Popular Courses & Classes

LSAT Courses & Classes in Denver, GRE Courses & Classes in Denver, SSAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Washington DC, SSAT Courses & Classes in Boston, Spanish Courses & Classes in Seattle, Spanish Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Chicago, LSAT Courses & Classes in Seattle, MCAT Courses & Classes in Washington DC

Popular Test Prep

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

High School Math : High School Math

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #11 : Factoring Radicals

Example Question #25 : Radicals

Example Question #1271 : High School Math

Example Question #31 : Radicals

Example Question #1 : Factoring Radicals

Example Question #1272 : High School Math

Example Question #12 : Simplifying Radicals

Example Question #82 : Algebra Ii

Example Question #1273 : High School Math

Example Question #1274 : High School Math

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: