We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Middle Level Quantitative : Squares / Square Roots

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

Create An Account

All ISEE Middle Level Quantitative Resources

6 Diagnostic Tests 110 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find The Square Root

Give the square root of 256.

Possible Answers:

$\displaystyle 14$

$\displaystyle 22$

$\displaystyle 16$

$\displaystyle 24$

$\displaystyle 18$

Correct answer:

$\displaystyle 16$

Explanation:

$16\cdot16= 256$ $\displaystyle 16\cdot16= 256$ - that is, 16 squared is 256, making 16 the square root of 256 by definition.

Report an Error

Example Question #2 : Squares / Square Roots

Which is the greater quantity?

(a) $\sqrt{425 }$ $\displaystyle \sqrt{425 }$

(b) $\displaystyle 21$

Possible Answers:

(a) and (b) are equal

(a) is greater

(b) is greater

It is impossible to tell from the information given

Correct answer:

(b) is greater

Explanation:

$21^{2} = 21 \times 21 = 441$ $\displaystyle 21^{2} = 21 \times 21 = 441$, so $21 = \sqrt{441}$ $\displaystyle 21 = \sqrt{441}$

$\displaystyle 441 > 425$, so

$21 = \sqrt{441} > \sqrt{425}$ $\displaystyle 21 = \sqrt{441} > \sqrt{425}$

Report an Error

Example Question #3 : Squares / Square Roots

Which is the greater quantity?

(a) $6 \sqrt{ 7}$ $\displaystyle 6 \sqrt{ 7}$

(b) $7 \sqrt{6}$ $\displaystyle 7 \sqrt{6}$

Possible Answers:

(a) is greater

It is impossible to tell from the information given

(a) and (b) are equal

(b) is greater

Correct answer:

(b) is greater

Explanation:

(a) $\left (6 \sqrt{7} \right )^{2} = 6^{2}\left ( \sqrt{7} \right ) ^{2} = 36 \cdot 7 = 252$ $\displaystyle \left (6 \sqrt{7} \right )^{2} = 6^{2}\left ( \sqrt{7} \right ) ^{2} = 36 \cdot 7 = 252$, so $6 \sqrt{7} = \sqrt{ 252 }$ $\displaystyle 6 \sqrt{7} = \sqrt{ 252 }$

(b) $\left (7 \sqrt{6} \right )^{2} = 7^{2}\left ( \sqrt{6} \right ) ^{2} = 49 \cdot 6 = 294$ $\displaystyle \left (7 \sqrt{6} \right )^{2} = 7^{2}\left ( \sqrt{6} \right ) ^{2} = 49 \cdot 6 = 294$, so $7\sqrt{6} = \sqrt{ 294 }$ $\displaystyle 7\sqrt{6} = \sqrt{ 294 }$

$\displaystyle 294 > 252$,

$\sqrt{294 }> \sqrt{252}$ $\displaystyle \sqrt{294 }> \sqrt{252}$,

and

$7\sqrt{6} > 6 \sqrt{7}$ $\displaystyle 7\sqrt{6} > 6 \sqrt{7}$

Report an Error

Example Question #3 : Squares / Square Roots

Column A Column B

$\sqrt{100}$ $\displaystyle \sqrt{100}$ $\sqrt{10.0}$ $\displaystyle \sqrt{10.0}$

Possible Answers:

There is no relationship between the quantities.

The quantities are equal.

The quantity in Column A is greater.

The quantity in Column B is greater.

Correct answer:

The quantity in Column A is greater.

Explanation:

The square root of 100 is 10, while the square root of 10 is between the square root of 9 and 16, so about 4. Therefore, Column A has to be greater.

Report an Error

Example Question #193 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Which of the following is equal to $\sqrt{5^{2}+7^{2}+7}$ $\displaystyle \sqrt{5^{2}+7^{2}+7}$ ?

Possible Answers:

None of the other responses is correct.

$\displaystyle 8$

$\displaystyle 11$

$\displaystyle 10$

$\displaystyle 9$

Correct answer:

$\displaystyle 9$

Explanation:

$\sqrt{5^{2}+7^{2}+7}$ $\displaystyle \sqrt{5^{2}+7^{2}+7}$

$=\sqrt{25 +49+7}$ $\displaystyle =\sqrt{25 +49+7}$

$=\sqrt{81}$ $\displaystyle =\sqrt{81}$

$\displaystyle =9$

Report an Error

Example Question #6 : Squares / Square Roots

Which of the following is equal to $\sqrt{11^{2}+ 6 \cdot 8}$ $\displaystyle \sqrt{11^{2}+ 6 \cdot 8}$ ?

Possible Answers:

None of the other responses is correct.

$\displaystyle 15$

$\displaystyle 13$

$\displaystyle 14$

$\displaystyle 12$

Correct answer:

$\displaystyle 13$

Explanation:

$\sqrt{11^{2}+ 6 \cdot 8}$ $\displaystyle \sqrt{11^{2}+ 6 \cdot 8}$

$= \sqrt{121+ 6 \cdot 8}$ $\displaystyle = \sqrt{121+ 6 \cdot 8}$

$= \sqrt{121+ 48}$ $\displaystyle = \sqrt{121+ 48}$

$= \sqrt{169}$ $\displaystyle = \sqrt{169}$

=13 $\displaystyle =13$

Report an Error

Example Question #194 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Which of the following is equal to $\sqrt{2^{3}+ 6^{2}+10^{2}}$ $\displaystyle \sqrt{2^{3}+ 6^{2}+10^{2}}$ ?

Possible Answers:

$\displaystyle 12$

None of the other responses is correct.

$\displaystyle 13$

$\displaystyle 11$

$\displaystyle 14$

Correct answer:

$\displaystyle 12$

Explanation:

$\sqrt{2^{3}+ 6^{2}+10^{2}}$ $\displaystyle \sqrt{2^{3}+ 6^{2}+10^{2}}$

$=\sqrt{8+36 +100}$ $\displaystyle =\sqrt{8+36 +100}$

$=\sqrt{ 144}$ $\displaystyle =\sqrt{ 144}$

=12 $\displaystyle =12$

Report an Error

Example Question #8 : Squares / Square Roots

$V^{2} = 72$ $\displaystyle V^{2} = 72$; $\displaystyle V$ is positive.

Which is the greater quantity?

(a) $\displaystyle V$

(b) $\displaystyle 8$

Possible Answers:

(A) is greater

It is impossible to tell which is greater from the information given

(B) is greater

(A) and (B) are equal

Correct answer:

(A) is greater

Explanation:

Since $\displaystyle V$is positive, we can compare $\displaystyle V$ to 8 by comparing their squares.

$V^{2} = 72$ $\displaystyle V^{2} = 72$ and $8^{2} = 8 \times 8 = 64$ $\displaystyle 8^{2} = 8 \times 8 = 64$

$V^{2} > 8^{2}$ $\displaystyle V^{2} > 8^{2}$, so V>8 $\displaystyle V>8$, making (A) greater.

Report an Error

Example Question #4 : Squares / Square Roots

$F^{2}= 36$ $\displaystyle F^{2}= 36$

Which is the greater quantity?

(A) $\displaystyle F$

(B) $\displaystyle 4$

Possible Answers:

(B) is greater

(A) and (B) are equal

(A) is greater

It is impossible to tell which is greater from the information given

Correct answer:

It is impossible to tell which is greater from the information given

Explanation:

If $F^{2} = 36$ $\displaystyle F^{2} = 36$, then one of two things is true - either F = 6 $\displaystyle F = 6$ or F = -6 $\displaystyle F = -6$.

However, 6 > 4 $\displaystyle 6 > 4$ and -6<4 $\displaystyle -6< 4$, so it is impossibe to tell whether (A) or (B) is greater.

Report an Error

Example Question #5 : Squares / Square Roots

$Q^{2} = 49$ $\displaystyle Q^{2} = 49$

Which is the greater quantity?

(A) $\displaystyle Q$

(B) $\displaystyle -8$

Possible Answers:

It is impossible to tell which is greater from the information given

(B) is greater

(A) and (B) are equal

(A) is greater

Correct answer:

(A) is greater

Explanation:

If $Q^{2} = 49$ $\displaystyle Q^{2} = 49$, then one of two things is true - either Q=7 $\displaystyle Q=7$ or Q=- 7 $\displaystyle Q=- 7$. Since 7 > -8 $\displaystyle 7 > -8$ and -7 > -8 $\displaystyle -7 > -8$, Q > -8 $\displaystyle Q > -8$ either way, so (A) is greater.

Report an Error

View Tutors

Sakshi
Certified Tutor

Queen's University, Masters in Business Administration, Business, General.

View Tutors

Gabby
Certified Tutor

University of Oregon, Bachelor in Arts, Journalism. University of Oregon, Current Grad Student, Communication, General.

View Tutors

Grace
Certified Tutor

St John's University-New York, Bachelor in Arts, Psychology. University of Bridgeport, Masters in Education, Education.

All ISEE Middle Level Quantitative Resources

6 Diagnostic Tests 110 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SAT Tutors in Philadelphia, Reading Tutors in Philadelphia, LSAT Tutors in Seattle, ACT Tutors in Philadelphia, MCAT Tutors in San Diego, Algebra Tutors in Dallas Fort Worth, Statistics Tutors in Dallas Fort Worth, Chemistry Tutors in Seattle, French Tutors in San Francisco-Bay Area, LSAT Tutors in San Francisco-Bay Area

Popular Courses & Classes

ISEE Courses & Classes in Chicago, SAT Courses & Classes in Atlanta, SSAT Courses & Classes in Phoenix, ISEE Courses & Classes in Miami, ISEE Courses & Classes in Atlanta, MCAT Courses & Classes in Boston, SAT Courses & Classes in Seattle, SSAT Courses & Classes in San Diego, LSAT Courses & Classes in Denver, Spanish Courses & Classes in Los Angeles

Popular Test Prep

SAT Test Prep in Washington DC, MCAT Test Prep in San Francisco-Bay Area, ACT Test Prep in San Diego, SSAT Test Prep in Atlanta, GMAT Test Prep in Houston, SAT Test Prep in Philadelphia, SSAT Test Prep in Los Angeles, MCAT Test Prep in Philadelphia, SAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in New York City

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

ISEE Middle Level Quantitative : Squares / Square Roots

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #1 : How To Find The Square Root

Example Question #2 : Squares / Square Roots

Example Question #3 : Squares / Square Roots

Example Question #3 : Squares / Square Roots

Example Question #193 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #6 : Squares / Square Roots

Example Question #194 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #8 : Squares / Square Roots

Example Question #4 : Squares / Square Roots

Example Question #5 : Squares / Square Roots

All ISEE Middle Level Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: