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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
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What is the value of (sqrt(24 + 5 sqrt(23)))(sqrt(24 - 5 sqrt(23))?
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30 May 2021, 23:57
30 May 2021, 23:57
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Question Stats:
64% (01:28) correct
35% (01:39) wrong based on 34 sessions
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What is the value of (\(\sqrt{24 + 5\sqrt{23}})(\sqrt{24 - 5 \sqrt{23}}\))?
A. 48
B. \( \sqrt{24}\)
C. \(5 \sqrt{2}\)
D. 1
E. \(24 - 5 \sqrt{23}\)
A. 48
B. \( \sqrt{24}\)
C. \(5 \sqrt{2}\)
D. 1
E. \(24 - 5 \sqrt{23}\)
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What is the value of (sqrt(24 + 5 sqrt(23)))(sqrt(24 - 5 sqrt(23))?
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03 Jun 2021, 05:49
03 Jun 2021, 05:49
3
GeminiHeat wrote:
What is the value of (\(\sqrt{24 + 5\sqrt{23}})(\sqrt{24 - 5 \sqrt{23}}\))?
A. 48
B. \( \sqrt{24}\)
C. \(5 \sqrt{2}\)
D. 1
E. \(24 - 5 \sqrt{23}\)
A. 48
B. \( \sqrt{24}\)
C. \(5 \sqrt{2}\)
D. 1
E. \(24 - 5 \sqrt{23}\)
Key concept: \((\sqrt{x})(\sqrt{y}) = \sqrt{xy}\)
\(\sqrt{24 + 5\sqrt{23}})(\sqrt{24 - 5 \sqrt{23}}\)
\([(24 + 5\sqrt{23})(24 - 5\sqrt{23})]^{\frac{1}{2}}\)
\([24^2 - (5\sqrt{23})^2]^{\frac{1}{2}}\)
\(\sqrt{576 - 575} = 1\)
Hence, option D
What is the value of (sqrt(24 + 5 sqrt(23)))(sqrt(24 - 5 sqrt(23))?
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30 Aug 2021, 02:39
30 Aug 2021, 02:39
1
Hi guys , i simply squared both the terms to remove the root sign and then solved it .
Will that approach also work here?
At the end got 576 - 575
Will that approach also work here?
At the end got 576 - 575
