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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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(7+43+7-43)2 is equal to which of the following?  [#permalink]

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09 Jan 2019, 23:33
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[Math Revolution GMAT math practice question]

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

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

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 06 Jan 2015 Posts: 774 Location: India Concentration: Operations, Finance GPA: 3.35 WE: Information Technology (Computer Software) (7+43+7-43)2 is equal to which of the following? [#permalink] ### Show Tags Updated on: 11 Jan 2019, 07:11 1 1 MathRevolution wrote: [Math Revolution GMAT math practice question] $$(\sqrt{7+4√3}+\sqrt{7-4√3})^2$$ is equal to which of the following? $$A. 32$$ $$B. 30$$ $$C. 24$$ $$D. 16$$ $$E. 12$$ $$(\sqrt{7+4√3}+\sqrt{7-4√3})^2$$ ==> $$a^2+b^2+2ab$$ =$$7+4√3+7-4√3+2((\sqrt{7+4√3})(\sqrt{7-4√3})$$ =$$(a+b)(a-b)=a^2-b^2$$ =7+7+2(7^2-(√3*16)^2) =14+2 =16 Hence D _________________ आत्मनॊ मोक्षार्थम् जगद्धिताय च Resource: GMATPrep RCs With Solution Originally posted by NandishSS on 10 Jan 2019, 00:52. Last edited by NandishSS on 11 Jan 2019, 07:11, edited 1 time in total. Intern Joined: 16 Jul 2018 Posts: 3 Re: (7+43+7-43)2 is equal to which of the following? [#permalink] ### Show Tags 11 Jan 2019, 07:03 NandishSS wrote: =7+7+2(7^2-√3*16) =14+2 NandishSS Can you please explain how you reduced 2(7^2-√3*16) to 2? Director Joined: 06 Jan 2015 Posts: 774 Location: India Concentration: Operations, Finance GPA: 3.35 WE: Information Technology (Computer Software) Re: (7+43+7-43)2 is equal to which of the following? [#permalink] ### Show Tags 11 Jan 2019, 07:11 1 jedijodes wrote: NandishSS wrote: =7+7+2(7^2-√3*16) =14+2 NandishSS Can you please explain how you reduced 2(7^2-√3*16) to 2? (7^2-(√3*16)^2) 49-48=1 There was a typo so edited. _________________ आत्मनॊ मोक्षार्थम् जगद्धिताय च Resource: GMATPrep RCs With Solution Director Joined: 20 Mar 2018 Posts: 513 Location: Ghana Concentration: Finance, Real Estate Schools: Terry '22 (7+43+7-43)2 is equal to which of the following? [#permalink] ### Show Tags 11 Jan 2019, 08:10 1 ((7+4(3)^1/2)^1/2 + ((7-4(3)^1/2)^1/2)^2 is in the form (x+y)^2 Where x= (7+4(3)^1/2)^1/2 and y= (7-4(3)^1/2)^1/2 (x+y)^2 = x^2+y^2 +2(XY) (7+4(3)^1/2)+(7-4(3)^1/2)+2((7+4(3)^1/2)(7-4(3)^1/2)) (4(3)^1/2) crosses out Now we have 7+7+2(difference of squares) Diff of squares =((7)^2-(4(3)^1/2)^2)^1/2) =(49-16(3))^1/2 =1 Now 7+7+2(1)=16 Ans is D Posted from my mobile device _________________ Veritas valet et vincet Director Joined: 09 Mar 2018 Posts: 980 Location: India Re: (7+43+7-43)2 is equal to which of the following? [#permalink] ### Show Tags 11 Jan 2019, 10:04 MathRevolution wrote: [Math Revolution GMAT math practice question] $$(\sqrt{7+4√3}+\sqrt{7-4√3})^2$$ is equal to which of the following? $$A. 32$$ $$B. 30$$ $$C. 24$$ $$D. 16$$ $$E. 12$$ just a question of $$(a+b)^2$$ and a$$^2 - b ^2$$ = (a-b) (a+b) = 7+4√3+7-4√3 + 2 *$$\sqrt{7+4√3}$$ * $$\sqrt{7-4√3}$$ = 14 + 2 Ans D. _________________ If you notice any discrepancy in my reasoning, please let me know. Lets improve together. Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up. Manager Joined: 18 Oct 2018 Posts: 91 Location: India Concentration: Finance, International Business GMAT 1: 710 Q50 V36 GPA: 4 WE: Business Development (Retail Banking) Re: (7+43+7-43)2 is equal to which of the following? [#permalink] ### Show Tags 11 Jan 2019, 10:10 ((7+4(3)^1/2)^1/2 + ((7-4(3)^1/2)^1/2)^2 (a+b)^2= a^2+b^2+2*a*b Thus (7+4(3)^1/2)+(7-4(3)^1/2)+2((7+4(3)^1/2)(7-4(3)^1/2 Diff of squares =((7)^2-(4(3)^1/2)^2)^1/2) =(49-16(3))^1/2 =1 Now 7+7+2(1)=16 Ans is D Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 9018 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: (7+43+7-43)2 is equal to which of the following? [#permalink] ### Show Tags 13 Jan 2019, 17:03 => You should recall two properties about nested radicals: $$\sqrt{a+b+2√ab}= √a+√b,$$ $$\sqrt{a+b-2√ab}= √a-√b,$$ where $$a > b.$$ Together, these yield $$(\sqrt{7+4√3}+\sqrt{7-4√3})^2$$ $$= (\sqrt{7+2√12}+\sqrt{7-2√12})^2$$ $$= (√4+√3+√4-√3)^2$$ $$= (2√4)^2$$ $$= 16$$ Therefore, the answer is D. Answer: D _________________ MathRevolution: 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$79 for 1 month Online Course"
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Joined: 09 Apr 2020
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Re: (7+43+7-43)2 is equal to which of the following?  [#permalink]

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22 Apr 2020, 12:40
struggling to understand the difference of squares application here. how can you get 7^2 out as a^2 when the a, and the entire expression, is under the radical?

if it was just 7 - 4*sqrt(3), then I understand a^2 - b^2 is 49 - 48. but how can it be 49 - 48 if the entire expression is under the radical?
Re: (7+43+7-43)2 is equal to which of the following?   [#permalink] 22 Apr 2020, 12:40