• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 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 PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## (7+43+7-43)^2 is equal to which of the following? tagged by: Max@Math Revolution ##### 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? ## 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 Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$99 for 3 month Online Course
Free Resources-30 day online access & Diagnostic Test
Email to : info@mathrevolution.com

### GMAT/MBA Expert

GMAT Instructor
Joined
25 May 2010
Posted:
15025 messages
Followed by:
1859 members
13060
GMAT Score:
790
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
âˆš3 â‰ˆ 1.7.
7 + 4âˆš3 â‰ˆ 7 + (4)(1.7) = 13.8.
7 - 4âˆš3 â‰ˆ 7 - (4)(1.7) = 0.2.

Thus, the given expression can be approximated as follows:
(âˆš13.8 + âˆš0.2)Â² = a little more than 13.8.
Only D is viable.

_________________
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.
Student Review #1
Student Review #2
Student Review #3

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.

### GMAT/MBA Expert

GMAT Instructor
Joined
09 Oct 2010
Posted:
1125 messages
Followed by:
29 members
59
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

### GMAT/MBA Expert

Legendary Member
Joined
24 Jul 2015
Posted:
1947 messages
Followed by:
29 members
19
GMAT Score:
=>

$$\sqrt{a+b+2\sqrt{ab}}=\sqrt{a}+\sqrt{b}$$ ,
$$\sqrt{a+b-2\sqrt{ab}}=\sqrt{a}-\sqrt{b}$$ , where a > b.

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

_________________

Math Revolution
Finish GMAT Quant Section with 10 minutes to spare.
The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Only $99 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 ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 1808 messages Followed by: 14 members Upvotes: 43 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 + 4âˆš3 y^2 = 7 - 4âˆš3 Next we can determine the value of 2xy: 2(âˆš(7 + 4âˆš3)(âˆš(7 - 4âˆš3) 2âˆš[(7 + 4âˆš3)(7 - 4âˆš3)] Using the difference of squares, we have: 2âˆš[7^2 - (4âˆš3)^2] 2âˆš(49 - 48) = 2 Thus, the final value is: (7 + 4âˆš3) + (7 - 4âˆš3) + 2 = 16 Answer: D _________________ Scott Woodbury-Stewart Founder and CEO • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for \$0

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

### Top First Responders*

1 Jay@ManhattanReview 66 first replies
2 fskilnik@GMATH 50 first replies
3 Brent@GMATPrepNow 49 first replies
4 GMATGuruNY 32 first replies
5 Rich.C@EMPOWERgma... 26 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 fskilnik@GMATH

GMATH Teacher

109 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

97 posts
3 Max@Math Revolution

Math Revolution

94 posts
4 Jay@ManhattanReview

Manhattan Review

83 posts
5 GMATGuruNY

The Princeton Review Teacher

78 posts
See More Top Beat The GMAT Experts