Last visit was: 26 Sep 2026, 22:33 It is currently 26 Sep 2026, 22:33
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
705-805 (Hard)|   Algebra|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 26 Sep 2026
Posts: 113,941
Own Kudos:
843,816
 [21]
Given Kudos: 111,838
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,941
Kudos: 843,816
 [21]
If (x^2 + 9)^(1/2) + (x^2 - 3)^(1/2) = 6, what is the value of 10 Nov 2023, 04:48
1
Kudos
Add Kudos
20
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

61% (02:14) correct 39% (02:46) wrong based on 240 sessions

History

Date
Time
Result
Not Attempted Yet
If \(\sqrt{x^2+9}+\sqrt{x^2-3}=6\), what is the value of \(\sqrt{x^2+9}-\sqrt{x^2-3}\)?

A. \(1\)

B. \(2\)

C. \(3\)

D. \(4\)

E. \(5\)
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
VivekSri
User avatar
Joined: 01 May 2022
Last visit: 05 Feb 2026
Posts: 428
Own Kudos:
805
 [9]
Given Kudos: 117
Location: India
WE:Engineering (Consulting)
Posts: 428
Kudos: 805
 [9]
If (x^2 + 9)^(1/2) + (x^2 - 3)^(1/2) = 6, what is the value of 12 Nov 2023, 09:37
7
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Bunuel
If \(\sqrt{x^2+9}+\sqrt{x^2-3}=6\), what is the value of \(\sqrt{x^2+9}-\sqrt{x^2-3}\)?

A. \(1\)

B. \(2\)

C. \(3\)

D. \(4\)

E. \(5\)
Show more

OA is B

Posted from my mobile device
Attachments

Screenshot_20231112_220504_Samsung Notes.jpg
Screenshot_20231112_220504_Samsung Notes.jpg [ 158.44 KiB | Viewed 3331 times ]

General Discussion
User avatar
ZIX
User avatar
Joined: 30 Sep 2023
Last visit: 06 Sep 2026
Posts: 88
Own Kudos:
204
 [1]
Given Kudos: 526
Posts: 88
Kudos: 204
 [1]
If (x^2 + 9)^(1/2) + (x^2 - 3)^(1/2) = 6, what is the value of 08 Mar 2024, 23:51
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
­The point is that you have to recognise \(\sqrt{x^2 + 9} + \sqrt{x^2 - 3}\) and \(\sqrt{x^2 + 9} - \sqrt{x^2 - 3}\)­ are a lot like the property \((a)^2 - (b)^2 = (a+b)(a-b)\)
.
.
.
So, \((\sqrt{x^2 + 9} + \sqrt{x^2 - 3})(\sqrt{x^2 + 9} - \sqrt{x^2 - 3})\)­ = \((\sqrt{x^2 + 9})^2\) - \((\sqrt{x^2 - 3})^2\)­. Solve and you will get your answer as:
.
.
.
\((6)(\sqrt{x^2 + 9} - \sqrt{x^2 - 3}) = 12\)­
Therefore, the answer = 2
User avatar
Seb2m02
User avatar
Joined: 03 Oct 2023
Last visit: 12 Jun 2026
Posts: 34
Own Kudos:
41
Given Kudos: 139
Posts: 34
Kudos: 41
If (x^2 + 9)^(1/2) + (x^2 - 3)^(1/2) = 6, what is the value of 18 Aug 2025, 19:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I everyone, I have another solution the solution, we can notice that the result 6 = 4+2
So (1) -> x^2 + 9 = 4^2
(2) -> x^2 - 3 = 2^2
(1)+3x(2) give us 4x^2=28, so x^2=7

If we replace x^2 un the second expression give in the statement, we find that the answer is 2

Hope that help
User avatar
herxheys12
User avatar
Joined: 23 Feb 2026
Last visit: 24 Sep 2026
Posts: 18
Own Kudos:
5
Given Kudos: 7
Location: India
Schools: ISB '26 INSEAD Jan '27 Bocconi
GMAT Focus 1: 535 Q76 V78 DI75
GMAT Focus 2: 615 Q79 V83 DI80
Schools: ISB '26 INSEAD Jan '27 Bocconi
GMAT Focus 2: 615 Q79 V83 DI80
Posts: 18
Kudos: 5
If (x^2 + 9)^(1/2) + (x^2 - 3)^(1/2) = 6, what is the value of 21 Sep 2026, 10:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
To simplify, assume: √(x^2 + 9) = A
and, √(x^2 - 3) = B

Then, the question becomes: if A + B = 6, what is the value of A - B?

Multiple A - B on both sides
(A + B)(A - B) = 6(A - B)
A^2 - B^2 = 6(A - B)

Input values,

x^2 + 9 - x^2 + 3 = 6 (A - B)
12 = 6 (A - B)

Divide both sides by 6

A - B = 2,
√(x^2 + 9) - √(x^2 - 3) = 2

Answer; B
User avatar
pappal
User avatar
Joined: 24 Nov 2022
Last visit: 23 Sep 2026
Posts: 390
Own Kudos:
134
Given Kudos: 121
Posts: 390
Kudos: 134
If (x^2 + 9)^(1/2) + (x^2 - 3)^(1/2) = 6, what is the value of 23 Sep 2026, 12:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
well i tried this way (x^2+9)^1/2=A & (x^2-3)^1/2=B let A-B=?
we have A+B=6 or A=(6-B)
A-B=6-B-B=6-2B for sure this value must be even so choices A,C,E out
now if 6-2B=4 then B=1
(x^2-3)^1/2=1 OR x^2-3=1 OR x^2=4 but this value doesn't satisfy (x^2+9)^1/2 =13^2 as integer value so D out
so B
lets check (x^2-3)^1/2=2 or x^2-3=4 or x^2=7
which satisfies the condition as (7+9)^1/2+(7-3)^1/2=6
Moderator:
Bunuel
Math Expert
113941 posts