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M02-09

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Bunuel
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M02-09 [#permalink] New post   16 Sep 2014, 00:17
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88% (00:52) correct 12% (01:19) wrong based on 759 sessions
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If \(x\) is a positive number and \(2\sqrt{2}=\sqrt{\sqrt{x}-6}\), what is the value of \(x\)?

A. \(\frac{14}{\sqrt{2}}\)
B. \(14\)
C. \(169\)
D. \(196\)
E. \(225\)
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Bunuel
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Re M02-09 [#permalink] New post   16 Sep 2014, 00:17
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Official Solution:

If \(x\) is a positive number and \(2\sqrt{2}=\sqrt{\sqrt{x}-6}\), what is the value of \(x\)?

A. \(\frac{14}{\sqrt{2}}\)
B. \(14\)
C. \(169\)
D. \(196\)
E. \(225\)


First, square both sides of the equation to get: \(8=\sqrt{x}-6\);

After rearranging, we find: \(\sqrt{x} = 14\);

Squaring once more, we have: \(x = 196\).


Answer: D
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Re: M02-09 [#permalink] New post   26 Dec 2018, 10:54
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Best Explanation Ever. Bunnel is Genius.
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TheNightKing
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Re: M02-09 [#permalink] New post   30 Jan 2020, 08:55
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Bunuel wrote:
If \(x\) is a positive number and \(2\sqrt{2}=\sqrt{\sqrt{x}-6}\), then what is the value of \(x\)?

A. \(\frac{14}{\sqrt{2}}\)
B. \(14\)
C. \(169\)
D. \(196\)
E. \(225\)


USE OPTIONS!!

\(2\sqrt{2}=\sqrt{\sqrt{x}-6}\)

Ignore A for now. It's complicated.

14 is not possible because it is not a perfect square.

C gives us x as 13. 13-6 is 7 and that's not equal to LHS.

D gives us x as 14. 14-6 is 8. Taking square root of 8 gives us \(2\sqrt{2}\) and we cannot have multiple correct answers.

So D it is.
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Re: M02-09 [#permalink] New post   22 Oct 2023, 13:48
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I've revised the question and solution, incorporating additional details for improved clarity. I trust this makes it more comprehensible.
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Re: M02-09 [#permalink]
22 Oct 2023, 13:48
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