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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$149 for 3 month Online Course
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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.

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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.

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

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

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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 ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2801 messages Followed by: 18 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 scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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