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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 ## What is the value of tagged by: M7MBA ##### This topic has 1 expert reply and 0 member replies ### Top Member ## What is the value of What is the value of $$\left(\sqrt{7+\sqrt{29}}-\sqrt{7-\sqrt{29}}\right)^2?$$ $$A.-26$$ $$B.\ 2\sqrt{29}$$ $$C.\ 14-4\sqrt{5}$$ $$D.\ 14$$ $$E.\ 14+4\sqrt{5}$$ The OA is C . Experts, may you help me here and tell me how to find the correct answer? Please. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: What is the value of $$\left(\sqrt{7+\sqrt{29}}-\sqrt{7-\sqrt{29}}\right)^2?$$ $$A.-26$$ $$B.\ 2\sqrt{29}$$ $$C.\ 14-4\sqrt{5}$$ $$D.\ 14$$ $$E.\ 14+4\sqrt{5}$$ The OA is C . Experts, may you help me here and tell me how to find the correct answer? Please. Hi M7MBA, Let's take a look at your questions. $$\left(\sqrt{7+\sqrt{29}}-\sqrt{7-\sqrt{29}}\right)^2 ... (i)$$ To evaluate it we will be using the formula: $$\left(a-b\right)^2=a^2-2ab+b^2$$ Using this formula (i) can be written as: $$=\left(\sqrt{7+\sqrt{29}}\right)^2-2\left(\sqrt{7+\sqrt{29}}\right)\left(\sqrt{7-\sqrt{29}}\right)+\left(\sqrt{7-\sqrt{29}}\right)^2$$ $$=\left(7+\sqrt{29}\right)-2\left(\sqrt{\left(7+\sqrt{29}\right)\left(7-\sqrt{29}\right)}\right)+\left(7-\sqrt{29}\right)$$ $$=\left(7+\sqrt{29}\right)-2\left(\sqrt{\left(7\right)^2-\left(\sqrt{29}\right)^2}\right)+\left(7-\sqrt{29}\right)$$ $$=\left(7+\sqrt{29}\right)-2\left(\sqrt{49-29}\right)+\left(7-\sqrt{29}\right)$$ $$=\left(7+\sqrt{29}\right)-2\left(\sqrt{20}\right)+\left(7-\sqrt{29}\right)$$ Combining like terms: $$=7+7-\sqrt{29}+\sqrt{29}-2\left(\sqrt{20}\right)$$ $$=7+7-2\left(\sqrt{20}\right)$$ $$=14-2\left(\sqrt{20}\right)$$ $$=14-2\left(\sqrt{4\times5}\right)$$ $$=14-2\times2\sqrt{5}$$ $$=14-4\sqrt{5}$$ Therefore, Option C is correct. Hope it helps. I am available if you'd like any follow up. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • Free Veritas GMAT Class Experience Lesson 1 Live Free 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 • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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