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\sqrt{20 + \sqrt{80}} =
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05 Jan 2016, 21:51
05 Jan 2016, 21:51
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72% (01:13) correct
27% (01:54) wrong based on 29 sessions
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\(\sqrt{20 + \sqrt{80}} =\)
A. \(4 \sqrt{5}\)
B. \(4 \sqrt{5 + \sqrt{5}}\)
C. \(4 \sqrt{5 \sqrt{5}}\)
D. \(2 \sqrt{5 + \sqrt{5}}\)
E. \(2 \sqrt{5} + 2 \sqrt{\sqrt5}\)
A. \(4 \sqrt{5}\)
B. \(4 \sqrt{5 + \sqrt{5}}\)
C. \(4 \sqrt{5 \sqrt{5}}\)
D. \(2 \sqrt{5 + \sqrt{5}}\)
E. \(2 \sqrt{5} + 2 \sqrt{\sqrt5}\)
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Joined: 16 May 2014
Posts: 590
Given Kudos: 0
GRE 1: Q165 V161
Re: Exponents & Roots
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06 Jan 2016, 02:46
06 Jan 2016, 02:46
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Expert Reply
Hello 'struggling with GRE',
I will solve the question step by step:
\(20 + \sqrt{80}\)
\(= 20 + \sqrt{16*5}\)
\(= 20 + \sqrt{4^2*5}\)
\(= 20 + 4\sqrt{5}\)
\(= 4*5 + 4\sqrt{5}\)
\(= 4(5 + \sqrt{5})\)
Therefore if you take a root of the above expression what you get is:
\(2\sqrt{(5 + sqrt(5))}\)
So the correct choice is D.
If this helps , let me know with kudos :D
I will solve the question step by step:
\(20 + \sqrt{80}\)
\(= 20 + \sqrt{16*5}\)
\(= 20 + \sqrt{4^2*5}\)
\(= 20 + 4\sqrt{5}\)
\(= 4*5 + 4\sqrt{5}\)
\(= 4(5 + \sqrt{5})\)
Therefore if you take a root of the above expression what you get is:
\(2\sqrt{(5 + sqrt(5))}\)
So the correct choice is D.
If this helps , let me know with kudos :D
Re: \sqrt{20 + \sqrt{80}} =
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25 Aug 2021, 04:08
25 Aug 2021, 04:08
Hello from the GRE Prep Club BumpBot!
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
