Last visit was: 22 Sep 2026, 20:39 It is currently 22 Sep 2026, 20:39
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
605-655 (Medium)|   Algebra|   Roots|      
User avatar
taha1234
User avatar
Joined: 27 Sep 2019
Last visit: 11 May 2025
Posts: 48
Own Kudos:
262
 [27]
Given Kudos: 661
Location: India
Schools: Rotman '26 Sauder'26
Schools: Rotman '26 Sauder'26
Posts: 48
Kudos: 262
 [27]
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.
Kudos
Add Kudos
27
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
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:

66% (01:52) correct 34% (02:28) wrong based on 1086 sessions

History

Date
Time
Result
Not Attempted Yet
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. \(18+5\sqrt{13}\)
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
Harshani
User avatar
Joined: 16 Oct 2016
Last visit: 24 Jan 2024
Posts: 32
Own Kudos:
47
 [11]
Given Kudos: 90
Location: Saudi Arabia
GMAT 1: 460 Q30 V23
GMAT 2: 500 Q39 V20
GMAT 2: 500 Q39 V20
Posts: 32
Kudos: 47
 [11]
What is the value of (9 - 65^(1/2))^(1/2) - (9 + 65^(1/2))^(1/2)^2 ? 27 Sep 2023, 12:55
6
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
To simplify I let x = SQRT (65)
See image for explanation.
Attachments

File comment: ans
answer 2.jpg
answer 2.jpg [ 450.17 KiB | Viewed 6170 times ]

User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Sep 2026
Posts: 113,782
Own Kudos:
843,026
 [6]
Given Kudos: 111,742
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,782
Kudos: 843,026
 [6]
What is the value of (9 - 65^(1/2))^(1/2) - (9 + 65^(1/2))^(1/2)^2 ? 07 Jul 2021, 02:18
2
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
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. \(18+5\sqrt{13}\)
Show more


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

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

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

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

Answer: A.
General Discussion
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,259
Own Kudos:
1,162
Posts: 39,259
Kudos: 1,162
What is the value of (9 - 65^(1/2))^(1/2) - (9 + 65^(1/2))^(1/2)^2 ? 06 Nov 2025, 12:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderator:
Bunuel
Math Expert
113782 posts