• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

(7+43+7-43)^2 is equal to which of the following?

This topic has 4 expert replies and 0 member replies

GMAT/MBA Expert

(7+43+7-43)^2 is equal to which of the following?

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



$$\left(\sqrt{7+4\sqrt{3}}+\sqrt{7-4\sqrt{3}}\right)^2$$ is equal to which of the following?

A. 32
B. 30
C. 24
D. 16
E. 12

_________________

Math Revolution
Finish GMAT Quant Section with 10 minutes to spare.
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $149 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Max@Math Revolution wrote:
$$\left(\sqrt{7+4\sqrt{3}}+\sqrt{7-4\sqrt{3}}\right)^2$$ is equal to which of the following?

A. 32
B. 30
C. 24
D. 16
E. 12
√3 ≈ 1.7.
7 + 4√3 ≈ 7 + (4)(1.7) = 13.8.
7 - 4√3 ≈ 7 - (4)(1.7) = 0.2.

Thus, the given expression can be approximated as follows:
(√13.8 + √0.2)² = a little more than 13.8.
Only D is viable.

The correct answer is D.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
Post
Max@Math Revolution wrote:
$$\left(\sqrt{7+4\sqrt{3}}+\sqrt{7-4\sqrt{3}}\right)^2$$ is equal to which of the following?

A. 32
B. 30
C. 24
D. 16
E. 12
$$? = {\left( {\sqrt {7 + 4\sqrt 3 } + \sqrt {7 - 4\sqrt 3 } } \right)^2} = {\left( {A + B} \right)^2}$$
$${A^2} = 7 + 4\sqrt 3 $$
$${B^2} = 7 - 4\sqrt 3 $$
$$2AB = 2\sqrt {\left( {7 + 4\sqrt 3 } \right)\left( {7 - 4\sqrt 3 } \right)} = 2\sqrt {{7^2} - {{\left( {4\sqrt 3 } \right)}^2}} = 2\sqrt {49 - 48} = 2$$
$$? = \left( {7 + 4\sqrt 3 } \right) + \left( {7 - 4\sqrt 3 } \right) + 2 = 16$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

_________________
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Legendary Member
Joined
24 Jul 2015
Posted:
2036 messages
Followed by:
29 members
Upvotes:
19
GMAT Score:
Most Active Expert
Post
=>

You should recall two properties about nested radicals:
$$\sqrt{a+b+2\sqrt{ab}}=\sqrt{a}+\sqrt{b}$$ ,
$$\sqrt{a+b-2\sqrt{ab}}=\sqrt{a}-\sqrt{b}$$ , where a > b.

Together, these yield
$$\left(\sqrt{7+4\sqrt{3}}+\sqrt{7-4\sqrt{3}}\right)^2$$
$$=\left(\sqrt{7+2\sqrt{12}}+\sqrt{7-2\sqrt{12}}\right)^2$$
$$=\left(\sqrt{4}+\sqrt{3}+\sqrt{4}-\sqrt{3}\right)^2$$
$$=\left(2\sqrt{4}\right)^2$$
$$=16$$

Therefore, the answer is D.
Answer: D

_________________

Math Revolution
Finish GMAT Quant Section with 10 minutes to spare.
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $149 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Unlimited Access to over 120 free video lessons-try it yourself
Email to : info@mathrevolution.com

  • +1 Upvote Post
  • Quote
  • Flag
Post
Max@Math Revolution wrote:
$$\left(\sqrt{7+4\sqrt{3}}+\sqrt{7-4\sqrt{3}}\right)^2$$ is equal to which of the following?

A. 32
B. 30
C. 24
D. 16
E. 12
We can look at the given expression as the quadratic identity of (x + y)^2 = x^2 + y^2 + 2xy, and thus:

x^2 = 7 + 4√3

y^2 = 7 - 4√3

Next we can determine the value of 2xy:

2(√(7 + 4√3)(√(7 - 4√3)

2√[(7 + 4√3)(7 - 4√3)]

Using the difference of squares, we have:

2√[7^2 - (4√3)^2]

2√(49 - 48) = 2

Thus, the final value is:

(7 + 4√3) + (7 - 4√3) + 2 = 16

Answer: D

_________________
Scott Woodbury-Stewart Founder and CEO

  • +1 Upvote Post
  • Quote
  • Flag
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors

Top First Responders*

1 fskilnik@GMATH 55 first replies
2 GMATGuruNY 52 first replies
3 Brent@GMATPrepNow 51 first replies
4 Jay@ManhattanReview 39 first replies
5 Rich.C@EMPOWERgma... 23 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

198 posts
2 image description fskilnik@GMATH

GMATH Teacher

154 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

97 posts
4 image description Max@Math Revolution

Math Revolution

89 posts
5 image description GMATGuruNY

The Princeton Review Teacher

76 posts
See More Top Beat The GMAT Experts