Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Squaring / Square Roots / Radicals

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 Next →

Example Question #1 : Square Of Difference

$\small (3a-2b)^{2}$ can be rewritten as:

Possible Answers:

$\small 9a^{2}-4b^{2}$

$\small 9a^{2}+12ab+4b^{2}$

$\small 9a^{2}+4b^{2}$

$\small 9a^{2}-12ab+4b^{2}$

$\small 9a^{2}-6ab+4b^{2}$

Correct answer:

$\small 9a^{2}-12ab+4b^{2}$

Explanation:

Use the formula for solving the square of a difference, $\small (x-y)^{2}=x^{2}-2xy+y^{2}$ . In this case, $\small \small \small (3a-2b)^{2}=9a^{2}-12ab+4b^{2}$

Report an Error

Example Question #1 : Square Of Difference

Expand:

(2x-6)^2

Possible Answers:

2x^2-12x+24

4x-12

4x^2-24x+36

4x^2-12x+36

Correct answer:

4x^2-24x+36

Explanation:

To multiply a difference squared, square the first term and add two times the multiplication of the two terms. Then add the second term squared.

(2x^)^2+2(2x)(-6)+(-6)^2=4x^2-24x+36

Report an Error

Example Question #1 : How To Find The Square Of Difference

The expression $\frac{x^2-25}{x^2+11x+30}$ is equivalent to:

Possible Answers:

$\frac{x-5}{x+6}$

$\frac{x+6}{x+5}$

$\frac{x-6}{x-5}$

x+6

$\frac{x+5}{x-6}$

Correct answer:

$\frac{x-5}{x+6}$

Explanation:

First, we need to factor the numerator and denominator separately and cancel out similar terms. We will start with the numerator because it can be factored easily as the difference of two squares.

x^2 - 25 = (x + 5)(x - 5)

Now factor the quadratic in the denominator.

x^2 + 11x + 30 = (x + 5)(x + 6)

Substitute these factorizations back into the original expression.

$\frac{(x+5)(x-5)}{(x+5)(x+6)}$

The (x+5) terms cancel out, leaving us with the following answer:

$\frac{x-5}{x+6}$

Report an Error

Example Question #1 : How To Find The Square Of A Sum

Evaluate the following expression:

$2^{5}+(5*2)^{2}$

Possible Answers:

164

132

110

Correct answer:

132

Explanation:

2 raised to the power of 5 is the same as multiplying 2 by itself 5 times so:

2⁵= 2x2x2x2x2 = 32

Then, 5x2 must first be multiplied before taking the exponent, yielding 10²= 100.

100 + 32 = 132

Report an Error

Example Question #1 : How To Find The Square Of A Sum

Expand:

(3x+5)^2

Possible Answers:

9x^2+30x+25

6x+10

9x^2-30x+25

9x^2+25

Correct answer:

9x^2+30x+25

Explanation:

To multiply a difference squared, square the first term and add two times the multiplication of the two terms. Then add the second term squared.

(3x)^2+2(3x)(5)+(5)^2=9x^2+30x+25

Report an Error

Example Question #3 : How To Find The Square Of A Sum

Which of the following is the square of 4x + 7y ?

Possible Answers:

$16x^{2}+ 22xy+ 49y^{2}$

$16x^{2} + 49y^{2}$

$16x^{2}+ 11xy+ 49y^{2}$

$16x^{2}+ 28xy+ 49y^{2}$

$16x^{2}+ 56xy+ 49y^{2}$

Correct answer:

$16x^{2}+ 56xy+ 49y^{2}$

Explanation:

Use the square of a sum pattern, substituting for and for in the pattern:

$(A+ B)^{2}= A^{2}+ 2AB + B^{2}$

$(4x + 7y)^{2}= (4x)^{2}+ 2 (4x) (7y) + (7y)^{2}$

$= 16x^{2}+ 56xy + 49y^{2}$

Report an Error

Example Question #4 : How To Find The Square Of A Sum

Which of the following is the square of $5 \sqrt{x} +3 \sqrt{y}$ ?

You may assume both and are positive.

Possible Answers:

25x + 9y

$25x + 9y+ 15\sqrt{xy}$

$5x + 3y+ 30\sqrt{xy}$

$5x + 3y+ 15\sqrt{xy}$

$25x + 9y+ 30 \sqrt{xy}$

Correct answer:

$25x + 9y+ 30 \sqrt{xy}$

Explanation:

Use the square of a sum pattern, substituting $5 \sqrt{x}$ for and $3 \sqrt{y}$ for in the pattern:

$(A+ B)^{2}= A^{2}+ 2AB + B^{2}$

$(5 \sqrt{x}+3 \sqrt{y})^{2}= (5 \sqrt{x})^{2}+ 2 (5 \sqrt{x})\left (3 \sqrt{y} \right ) + \left (3 \sqrt{y} \right )^{2}$

$(5 \sqrt{x}+3 \sqrt{y})^{2}= 25x+ 30 \sqrt{xy} + 9y$

$25x + 9y+ 30 \sqrt{xy}$

Report an Error

Example Question #5 : How To Find The Square Of A Sum

Which of the following is the square of $x^{2}+ x + 7$ ?

Possible Answers:

$x^{4}+ x^{2}+ 49$

$x^{4}+ x^{3}+14x^{2}+7x+49$

$x^{4}+2x^{3}+15x^{2}+14x+49$

$x^{4}+2x^{3}+8x^{2}+8x+49$

$x^{4}+ x^{3}+14x^{2}+14x+49$

Correct answer:

$x^{4}+2x^{3}+15x^{2}+14x+49$

Explanation:

Multiply vertically as follows:

$\begin{matrix} x^{2}+ \; \; \; x +\; \; \; 7\\\underline{x^{2}+\; \; \; x +\; \; \; 7} \end{matrix}$

$7 x^{2}+7 x +49$

$x^{3}+ x^{2} + 7x$

$\underline{x^{4}+ x^{3}+7 x^{2} \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; }$

$x^{4}+2x^{3}+15x^{2}+14x+49$

Report an Error

Example Question #6 : How To Find The Square Of A Sum

Which of the following is the square of $y + \sqrt{17}$ ?

Possible Answers:

$y^{2}+ y\sqrt{17}+17$

$y^{2}+ 34y+17$

$y^{2}+ 17y+17$

The correct answer is not given among the other responses.

$y^{2}+ y\sqrt{34}+17$

Correct answer:

The correct answer is not given among the other responses.

Explanation:

Use the square of a sum pattern, substituting for and $\sqrt{17}$ for in the pattern:

$(A+ B)^{2}= A^{2}+ 2AB + B^{2}$

$(y + \sqrt{17})^{2}= y^{2}+ 2y \sqrt{17} + (\sqrt{17})^{2}$

$(y + \sqrt{17})^{2}= y^{2}+ 2y \sqrt{17} + 17$

This is not equivalent to any of the given choices.

Report an Error

Example Question #7 : How To Find The Square Of A Sum

Which of the following is the square of $\frac{1}{4}x + \frac{1}{7}$ ?

Possible Answers:

$\frac{1}{16}x ^{2}+ \frac{1}{28}x +\frac{1}{49}$

$\frac{1}{16}x ^{2}+ \frac{1}{14}x +\frac{1}{49}$

$\frac{1}{8}x ^{2}+ \frac{1}{14}x +\frac{1}{14}$

$\frac{1}{16}x ^{2}+ \frac{1}{56}x +\frac{1}{49}$

$\frac{1}{8}x ^{2}+ \frac{1}{28}x +\frac{1}{14}$

Correct answer:

$\frac{1}{16}x ^{2}+ \frac{1}{14}x +\frac{1}{49}$

Explanation:

Use the square of a sum pattern, substituting $5 \sqrt{x}$ for and $3 \sqrt{y}$ for in the pattern:

$(A+ B)^{2}= A^{2}+ 2AB + B^{2}$

$\left (\frac{1}{4}x + \frac{1}{7} \right )^{2}= \left (\frac{1}{4}x \right )^{2}+ 2 \left (\frac{1}{4}x \right )\left (\frac{1}{7} \right ) + \left (\frac{1}{7} \right )^{2}$

$= \frac{1}{16}x ^{2}+ \frac{1}{14}x +\frac{1}{49}$

Report an Error

← Previous 1 2 3 4 5 Next →

View ACT Math Tutors

A.J.
Certified Tutor

The University of Alabama, Bachelor in Arts, Economics. University of Virginia-Main Campus, Juris Doctor, Legal Studies.

View ACT Math Tutors

Meet
Certified Tutor

Lakehead University, Bachelor, Mathematics.

View ACT Math Tutors

Yibin
Certified Tutor

University of Sheffield, Master of Science, Robotics Technology.

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

Popular Courses & Classes

MCAT Courses & Classes in New York City, LSAT Courses & Classes in Houston, SAT Courses & Classes in Denver, SAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Phoenix, GMAT Courses & Classes in Los Angeles, GMAT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Seattle, ISEE Courses & Classes in Seattle, SSAT Courses & Classes in Washington DC

Popular Test Prep

GRE Test Prep in Dallas Fort Worth, ACT Test Prep in Miami, ISEE Test Prep in Denver, GMAT Test Prep in Miami, GMAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Seattle, ISEE Test Prep in San Francisco-Bay Area, GRE Test Prep in Chicago, SSAT Test Prep in Dallas Fort Worth, GMAT Test Prep in Dallas Fort Worth

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

ACT Math : Squaring / Square Roots / Radicals

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Square Of Difference

Example Question #1 : Square Of Difference

Example Question #1 : How To Find The Square Of Difference

Example Question #1 : How To Find The Square Of A Sum

Example Question #1 : How To Find The Square Of A Sum

Example Question #3 : How To Find The Square Of A Sum

Example Question #4 : How To Find The Square Of A Sum

Example Question #5 : How To Find The Square Of A Sum

Example Question #6 : How To Find The Square Of A Sum

Example Question #7 : How To Find The Square Of A Sum

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: