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01 Nov 2010, 20:27
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
67% (01:49) correct
33%
(02:09)
wrong
based on 1634
sessions
History
Date
Time
Result
Not Attempted Yet
What is the value of \((\sqrt{7+\sqrt{29}}-\sqrt{7-\sqrt{29}})^2\)
A. -26
B. \(2\sqrt{29}\)
C. \(14 - 4\sqrt{5}\)
D. 14
E. \(14 + 4\sqrt{5}\)
solve.jpg [ 7.1 KiB | Viewed 26115 times ]
A. -26
B. \(2\sqrt{29}\)
C. \(14 - 4\sqrt{5}\)
D. 14
E. \(14 + 4\sqrt{5}\)
Attachment:
solve.jpg [ 7.1 KiB | Viewed 26115 times ]
01 Nov 2010, 20:38
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What is the value of \((\sqrt{7+\sqrt{29}}-\sqrt{7-\sqrt{29}})^2\)
A. -26
B. \(2\sqrt{29}\)
C. \(14 - 4\sqrt{5}\)
D. 14
E. \(14 + 4\sqrt{5}\)
You should apply two properties:
\((a-b)^2=a^2-2ab+b^2\);
\((a+b)(a-b)=a^2-b^2\)
\((\sqrt{7+\sqrt{29}}-\sqrt{7-\sqrt{29}})^2=(\sqrt{7+\sqrt{29}})^2-2(\sqrt{(7+\sqrt{29})(7-\sqrt{29})}+(\sqrt{7-\sqrt{29}})^2=\)
\(=7+\sqrt{29}-2\sqrt{49-29}+7-\sqrt{29}=14-2\sqrt{20}=14-4\sqrt{5}\).
Answer: C.
A. -26
B. \(2\sqrt{29}\)
C. \(14 - 4\sqrt{5}\)
D. 14
E. \(14 + 4\sqrt{5}\)
You should apply two properties:
\((a-b)^2=a^2-2ab+b^2\);
\((a+b)(a-b)=a^2-b^2\)
\((\sqrt{7+\sqrt{29}}-\sqrt{7-\sqrt{29}})^2=(\sqrt{7+\sqrt{29}})^2-2(\sqrt{(7+\sqrt{29})(7-\sqrt{29})}+(\sqrt{7-\sqrt{29}})^2=\)
\(=7+\sqrt{29}-2\sqrt{49-29}+7-\sqrt{29}=14-2\sqrt{20}=14-4\sqrt{5}\).
Answer: C.
General Discussion
bp2013
Joined: 07 May 2015
Last visit: 13 Oct 2019
Posts: 29
Own Kudos:
Schools: Booth PT '22 (D) Kellogg PT '22 (A)
20 Apr 2018, 08:03
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Bunuel
I've been going over this and can't seem to wrap my head around this part:
(\sqrt{7+[square_root]29}[/square_root])^2 <---- isn't this another a^2 + b^2 + 2ab? why did this reduce to just 7+\sqrt{29}?
