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605-655 (Medium)|   Algebra|   Roots|      
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taha1234
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What is the value of (9 - 65^(1/2))^(1/2) - (9 + 65^(1/2))^(1/2)^2 ? Updated on: 07 Jul 2021, 02:13
Originally posted by taha1234 on 07 Jul 2021, 02:08.
Last edited by Bunuel on 07 Jul 2021, 02:13, edited 1 time in total.
Renamed the topic and edited the question.
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A
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45% (medium)

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66% (01:51) correct 34% (02:29) wrong based on 1061 sessions

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What is the value of \((\sqrt{9-\sqrt{65}}- \sqrt{9+\sqrt{65}})^2\)?

A. 10
B. \(\sqrt{65}\)
C. \(18-5\sqrt{13}\)
D. 18
E. \(18+5\sqrt{13}\)
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A
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What is the value of (9 - 65^(1/2))^(1/2) - (9 + 65^(1/2))^(1/2)^2 ? 27 Sep 2023, 12:55
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To simplify I let x = SQRT (65)
See image for explanation.
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What is the value of (9 - 65^(1/2))^(1/2) - (9 + 65^(1/2))^(1/2)^2 ? 07 Jul 2021, 02:18
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taha1234
What is the value of \((\sqrt{9-\sqrt{65}}- \sqrt{9+\sqrt{65}})^2\)?

A. 10
B. \(\sqrt{65}\)
C. \(18-5\sqrt{13}\)
D. 18
E. \(18+5\sqrt{13}\)
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\((\sqrt{9-\sqrt{65}}- \sqrt{9+\sqrt{65}})^2 =\)

\(=(\sqrt{9-\sqrt{65}})^2 -2*(\sqrt{9-\sqrt{65}})(\sqrt{9+\sqrt{65}}) + (\sqrt{9+\sqrt{65}})^2 =\)

\(=(9-\sqrt{65}) -2*(\sqrt{9^2-\sqrt{65}^2}) + (9+\sqrt{65}) =\)

\(=18 -2*(\sqrt{81-65})=18-8=10\)

Answer: A.
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What is the value of (9 - 65^(1/2))^(1/2) - (9 + 65^(1/2))^(1/2)^2 ? 06 Nov 2025, 12:50
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