Last visit was: 23 Apr 2026, 09:00 It is currently 23 Apr 2026, 09:00
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
   1   2 
User avatar
singhall
User avatar
Joined: 01 Apr 2023
Last visit: 02 May 2024
Posts: 137
Own Kudos:
74
Given Kudos: 134
Location: India
Concentration: General Management, Technology
Schools: IIMC  (A) IIM PGPBL '25 (I)
GMAT 1: 680 Q48 V35
GPA: 3.58
Products:
My Reviews
Schools: IIMC  (A) IIM PGPBL '25 (I)
GMAT 1: 680 Q48 V35
Posts: 137
Kudos: 74
M06-02 28 Jun 2023, 22:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
rsamant
Why do we use absolute signs in this problem??

Because \(\sqrt{x^2}=|x|\). Check for more Absolute value tips: https://gmatclub.com/forum/absolute-val ... 75002.html


Theory on Abolute Values: https://gmatclub.com/forum/math-absolut ... 86462.html

DS Abolute Values Questions to practice: https://gmatclub.com/forum/search.php?s ... &tag_id=37
PS Abolute Values Questions to practice: https://gmatclub.com/forum/search.php?s ... &tag_id=58

Hope this helps.
Show more


What is the difference between Because \(\sqrt{x^2}=|x|\) and Mathematically the square root function cannot give negative result. When the GMAT provides the square root sign for an even root, then the only accepted answer is the positive root.
I got the second explanation in a different question. https://gmatclub.com/forum/d01-183474.html

Even roots have only a positive value on the GMAT.

These two statements are creating a contradiction in my head. Can someone please help me clear the difference between these two?

Thanks!
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,779
Own Kudos:
810,802
Given Kudos: 105,853
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,779
Kudos: 810,802
M06-02 28 Jun 2023, 23:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
singhall
Bunuel
rsamant
Why do we use absolute signs in this problem??

Because \(\sqrt{x^2}=|x|\). Check for more Absolute value tips: https://gmatclub.com/forum/absolute-val ... 75002.html


Theory on Abolute Values: https://gmatclub.com/forum/math-absolut ... 86462.html

DS Abolute Values Questions to practice: https://gmatclub.com/forum/search.php?s ... &tag_id=37
PS Abolute Values Questions to practice: https://gmatclub.com/forum/search.php?s ... &tag_id=58

Hope this helps.


What is the difference between Because \(\sqrt{x^2}=|x|\) and Mathematically the square root function cannot give negative result. When the GMAT provides the square root sign for an even root, then the only accepted answer is the positive root.
I got the second explanation in a different question. https://gmatclub.com/forum/d01-183474.html

Even roots have only a positive value on the GMAT.

These two statements are creating a contradiction in my head. Can someone please help me clear the difference between these two?

Thanks!
Show more

What's causing the confusion? The square root symbol, or any even root such as the fourth root, cannot yield a negative result. Therefore, \(\sqrt{x^2}=|x|\), not simply x. This is because x can be negative, while |x| cannot.
User avatar
singhall
User avatar
Joined: 01 Apr 2023
Last visit: 02 May 2024
Posts: 137
Own Kudos:
74
Given Kudos: 134
Location: India
Concentration: General Management, Technology
Schools: IIMC  (A) IIM PGPBL '25 (I)
GMAT 1: 680 Q48 V35
GPA: 3.58
Products:
My Reviews
Schools: IIMC  (A) IIM PGPBL '25 (I)
GMAT 1: 680 Q48 V35
Posts: 137
Kudos: 74
M06-02 29 Jun 2023, 11:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
singhall
Bunuel
Why do we use absolute signs in this problem??

Because \(\sqrt{x^2}=|x|\). Check for more Absolute value tips: https://gmatclub.com/forum/absolute-val ... 75002.html





What is the difference between Because \(\sqrt{x^2}=|x|\) and Mathematically the square root function cannot give negative result. When the GMAT provides the square root sign for an even root, then the only accepted answer is the positive root.
I got the second explanation in a different question. https://gmatclub.com/forum/d01-183474.html

Even roots have only a positive value on the GMAT.

These two statements are creating a contradiction in my head. Can someone please help me clear the difference between these two?

Thanks!

What's causing the confusion? The square root symbol, or any even root such as the fourth root, cannot yield a negative result. Therefore, \(\sqrt{x^2}=|x|\), not simply x. This is because x can be negative, while |x| cannot.
Show more

Thanks for your response Bunuel
Okay, understood, I was confused because we were putting \(\sqrt{(y+1)^2}\) as |y+1| and not simply (y+1). Makes sense.
We can write \(\sqrt{y^2}\) as y but \(\sqrt{ (y+1)^2 } \) as |y+1| is so because y if less than -1 would yield a negative result.
Am I on the right track now?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,779
Own Kudos:
810,802
Given Kudos: 105,853
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,779
Kudos: 810,802
M06-02 05 Jul 2023, 00:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
singhall
Bunuel
singhall
Because \(\sqrt{x^2}=|x|\). Check for more Absolute value tips: https://gmatclub.com/forum/absolute-val ... 75002.html





What is the difference between Because \(\sqrt{x^2}=|x|\) and Mathematically the square root function cannot give negative result. When the GMAT provides the square root sign for an even root, then the only accepted answer is the positive root.
I got the second explanation in a different question. https://gmatclub.com/forum/d01-183474.html

Even roots have only a positive value on the GMAT.

These two statements are creating a contradiction in my head. Can someone please help me clear the difference between these two?

Thanks!

What's causing the confusion? The square root symbol, or any even root such as the fourth root, cannot yield a negative result. Therefore, \(\sqrt{x^2}=|x|\), not simply x. This is because x can be negative, while |x| cannot.

Thanks for your response Bunuel
Okay, understood, I was confused because we were putting \(\sqrt{(y+1)^2}\) as |y+1| and not simply (y+1). Makes sense.
We can write \(\sqrt{y^2}\) as y but \(\sqrt{ (y+1)^2 } \) as |y+1| is so because y if less than -1 would yield a negative result.
Am I on the right track now?
Show more

No. The following is always true: \(\sqrt{x^2}=|x|\).

For instance, of x = 5, then \(\sqrt{x^2}=|x|=5\) and if x = -5, then \(\sqrt{x^2}=|x|=5\).
User avatar
BottomJee
User avatar
Retired Moderator
Joined: 05 May 2019
Last visit: 09 Jun 2025
Posts: 994
Own Kudos:
1,457
Given Kudos: 1,009
Affiliations: GMAT Club
Location: India
GMAT Focus 1: 645 Q82 V81 DI82
GMAT 1: 430 Q31 V19
GMAT 2: 570 Q44 V25
GMAT 3: 660 Q48 V33
GPA: 3.26
WE:Engineering (Manufacturing)
Products:
My Reviews
GMAT Focus 1: 645 Q82 V81 DI82
GMAT 3: 660 Q48 V33
Posts: 994
Kudos: 1,457
M06-02 12 Aug 2023, 09:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I think this is a high-quality question and I agree with explanation.
User avatar
depjsr31
User avatar
Joined: 22 Dec 2024
Last visit: 17 Apr 2025
Posts: 6
Own Kudos:
9
Given Kudos: 1
Posts: 6
Kudos: 9
M06-02 08 Jan 2025, 16:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
This question got my respect! :dazed :please:
User avatar
Testuhsjsj2673
User avatar
Joined: 07 Jan 2024
Last visit: 31 May 2025
Posts: 2
Given Kudos: 3
Posts: 2
Kudos: 0
M06-02 25 Jan 2025, 18:01
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I like the solution - it’s helpful.
User avatar
NSK1984
User avatar
School Moderator - Stanford MSx
Joined: 26 Dec 2023
Last visit: 04 Mar 2026
Posts: 102
Own Kudos:
25
Given Kudos: 19
GMAT Focus 1: 595 Q81 V81 DI76
GMAT Focus 2: 625 Q85 V81 DI77
GMAT Focus 3: 685 Q88 V84 DI80
WE:Engineering (Military)
GMAT Focus 3: 685 Q88 V84 DI80
Posts: 102
Kudos: 25
M06-02 18 May 2025, 19:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I like the solution - it’s helpful.
User avatar
DarkAster
User avatar
Joined: 21 Jul 2024
Last visit: 24 Feb 2026
Posts: 11
Own Kudos:
1
Given Kudos: 2
Location: India
Posts: 11
Kudos: 1
M06-02 23 Nov 2025, 09:22
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I like the solution - it’s helpful.
User avatar
sunshineeee
User avatar
Joined: 17 May 2020
Last visit: 09 Apr 2026
Posts: 96
Own Kudos:
22
Given Kudos: 223
Location: Indonesia
Schools: Stern '26 (WL) Tepper '26 (WL) BU'26 (A) Ross '26 Johnson '26
Schools: Stern '26 (WL) Tepper '26 (WL) BU'26 (A) Ross '26 Johnson '26
Posts: 96
Kudos: 22
M06-02 30 Nov 2025, 03:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I did not quite understand the solution. is |y-1| must be positive? Why can't it be negative?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,779
Own Kudos:
810,802
Given Kudos: 105,853
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,779
Kudos: 810,802
M06-02 30 Nov 2025, 04:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sunshineeee
I did not quite understand the solution. is |y-1| must be positive? Why can't it be negative?
Show more
Absolute value can never be negative, by definition it represents the distance from zero, and distance cannot be negative. That’s why |y - 1| is always ≥ 0, no matter what y is. If this feels unfamiliar, you should brush up your absolute-value basics.

Absolute Value

Theory

Questions

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
User avatar
DarkAster
User avatar
Joined: 21 Jul 2024
Last visit: 24 Feb 2026
Posts: 11
Own Kudos:
1
Given Kudos: 2
Location: India
Posts: 11
Kudos: 1
M06-02 02 Dec 2025, 22:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sunshineeee
I did not quite understand the solution. is |y-1| must be positive? Why can't it be negative?
Show more
In order words apart from what bb mentioned we can say |y-1| is the value of √(y-1)^2 in the real equation. So any value which is derived from square root of something which is a real number is always non-negative.
User avatar
_ankitchawla_
User avatar
Joined: 14 Dec 2023
Last visit: 22 Apr 2026
Posts: 15
Own Kudos:
2
Given Kudos: 62
Products:
GMAT Club Tests Forum Quiz
Posts: 15
Kudos: 2
M06-02 27 Jan 2026, 02:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I like the solution - it’s helpful.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,965
Own Kudos:
1,117
Posts: 38,965
Kudos: 1,117
M06-02 18 Mar 2026, 01:28
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.
   1   2 
Moderators:
Bunuel
Math Expert
109779 posts
bb
Founder
43154 posts