It is currently 10 Sep 2026, 07:39
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
User avatar
vannbj
User avatar
Joined: 18 Sep 2009
Last visit: 04 Oct 2015
Posts: 244
Status:Yeah well whatever.
Location: United States
GMAT 1: 660 Q42 V39
GMAT 2: 730 Q48 V42
GPA: 3.49
WE:Analyst (Insurance)
GMAT 2: 730 Q48 V42
Posts: 244
Of the following integers which is the closest approximation
Post URL
14 May 2010, 07:34
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
Official Answer and Stats are available only to registered users. Register/Login.
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

73% (00:53) correct 27% (00:55) wrong based on 3526 sessions

History

Date
Time
Result
Not Attempted Yet
Of the following integers, which is the closest approximation to \((\sqrt{2} + \sqrt{5})^2\)?

A. 7
B. 10
C. 13
D. 15
E. 17
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.
Need more similar questions? Run a 5 to 10 question quiz in GMAT Club Forum Quiz →

_________________
He that is in me > he that is in the world. - source 1 John 4:4
Signature Read More
12
Kudos
Add Kudos
125
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 10 Sep 2026
Posts: 113,384
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,384
Of the following integers which is the closest approximation
Post URL
15 May 2010, 02:05
vannbj
Of the following integers, which is the closest approximation to \((\sqrt{2} + \sqrt{5})^2\)?

7
10
13
15
17

How do you do this without a calculator?
Show more

\((\sqrt{2} + \sqrt{5})^2=2+2*\sqrt{2}*\sqrt{5}+5=7+2\sqrt{10}\)

Since \(\sqrt{10}\approx{3}\), then \(7+2\sqrt{10}\approx{7+6}=13\)

Answer: C.­­­

_________________
New to the GMAT Club?
Signature Read More
21
Kudos
Add Kudos
24
Bookmarks
Bookmark this Post
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 10 Sep 2026
Posts: 113,384
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,384
Of the following integers which is the closest approximation
Post URL
30 Mar 2015, 04:15
joaomario
Bunuel
vannbj
Of the following integers, which is the closest approximation to \((\sqrt{2} + \sqrt{5})^2\)?

7
10
13
15
17

How do you do this without a calculator?

\((\sqrt{2} + \sqrt{5})^2=2+2*\sqrt{2}*\sqrt{5}+5=7+2\sqrt{10}\) --> \(\sqrt{10}\approx{3}\) --> \(7+2\sqrt{10}\approx{7+6}=13\)

Answer: C.

How did you get 2[square_root]10? I expanded the original equation and went from [square_root]20 to 2[square_root]5.


Thanks for your help

More specifically this is how I approached it:

2 + [square_root]10 + [square_root]10 + 5
7 + [square_root]20
7 + [square_root]4 [square_root]5
7 + 2[square_root]5
9 + [square_root]5
Show more

I'm not exactly sure what you are doing there...

You should apply \((a+b)^2=a^2+2ab+b^2\).

Hope it helps.

_________________
New to the GMAT Club?
Signature Read More
5
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
General Discussion
User avatar
Zarrolou
User avatar
Joined: 02 Sep 2012
Last visit: 11 Dec 2013
Posts: 840
Status:Far, far away!
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Posts: 840
Of the following integers which is the closest approximation
Post URL
23 Apr 2013, 00:35
\((a+b)^2=(2+5+2\sqrt{10})=2+5+2*3=13\)

C
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
User avatar
joaomario
User avatar
Joined: 11 Aug 2014
Last visit: 03 Apr 2015
Posts: 3
Posts: 3
Of the following integers which is the closest approximation
Post URL
30 Mar 2015, 04:11
Bunuel
vannbj
Of the following integers, which is the closest approximation to \((\sqrt{2} + \sqrt{5})^2\)?

7
10
13
15
17

How do you do this without a calculator?

\((\sqrt{2} + \sqrt{5})^2=2+2*\sqrt{2}*\sqrt{5}+5=7+2\sqrt{10}\) --> \(\sqrt{10}\approx{3}\) --> \(7+2\sqrt{10}\approx{7+6}=13\)

Answer: C.
Show more

How did you get 2[square_root]10? I expanded the original equation and went from [square_root]20 to 2[square_root]5.


Thanks for your help

More specifically this is how I approached it:

2 + [square_root]10 + [square_root]10 + 5
7 + [square_root]20
7 + [square_root]4 [square_root]5
7 + 2[square_root]5
9 + [square_root]5
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
avatar
OptimusPrepJanielle
avatar
Joined: 06 Nov 2014
Last visit: 08 Sep 2017
Posts: 1,776
Expert
Expert reply
Posts: 1,776
Of the following integers which is the closest approximation
Post URL
31 Mar 2015, 11:14
vannbj
Of the following integers, which is the closest approximation to \((\sqrt{2} + \sqrt{5})^2\)?

A. 7
B. 10
C. 13
D. 15
E. 17
Show more
(sqrt(2) + sqrt(5))^2 =2 + 2*sqrt(2)*sqrt(5) + 5
= 7 + 2*sqrt(10)
= 7 + 2*3 (approximated to sqrt(9))
= 13
Hence option (C).

--
Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 09 Sep 2026
Posts: 22,737
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 22,737
Of the following integers which is the closest approximation
Post URL
18 Dec 2017, 07:45
Quote:
Of the following integers, which is the closest approximation to \((\sqrt{2} + \sqrt{5})^2\)?

7
10
13
15
17
Show more

We can FOIL (√2 + √5)^2 as (√2 + √5)(√2 + √5):

(√2 + √5)(√2 + √5)

= (√2)^2 + 2(√2)(√5) + (√5)^2

= 2 + 2(√10) + 5

≈ 7 + 2(3)

= 13

Answer: C

_________________
See why Target Test Prep is the top rated GMAT course on GMAT Club. Read Our Reviews
Signature Read More
3
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
User avatar
dave13
User avatar
Joined: 09 Mar 2016
Last visit: 09 Jul 2026
Posts: 1,081
Posts: 1,081
Of the following integers which is the closest approximation
Post URL
11 Jun 2018, 12:44
Bunuel
vannbj
Of the following integers, which is the closest approximation to \((\sqrt{2} + \sqrt{5})^2\)?

7
10
13
15
17

How do you do this without a calculator?

\((\sqrt{2} + \sqrt{5})^2=2+2*\sqrt{2}*\sqrt{5}+5=7+2\sqrt{10}\) --> \(\sqrt{10}\approx{3}\) --> \(7+2\sqrt{10}\approx{7+6}=13\)

Answer: C.
Show more


pushpitkc, is my approach correct ? :)

\(\sqrt{2} = 1.4\)

\(\sqrt{5}=2.2\)

\(2.2+1.4 = 3.6\)

\((3.6)^2 = 12.96\) apprx \(13\)
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
pushpitkc
User avatar
Joined: 26 Feb 2016
Last visit: 19 Feb 2025
Posts: 2,790
Location: India
GPA: 3.12
Posts: 2,790
Of the following integers which is the closest approximation
Post URL
11 Jun 2018, 12:47
dave13
Bunuel
vannbj
Of the following integers, which is the closest approximation to \((\sqrt{2} + \sqrt{5})^2\)?

7
10
13
15
17

How do you do this without a calculator?

\((\sqrt{2} + \sqrt{5})^2=2+2*\sqrt{2}*\sqrt{5}+5=7+2\sqrt{10}\) --> \(\sqrt{10}\approx{3}\) --> \(7+2\sqrt{10}\approx{7+6}=13\)

Answer: C.


pushpitkc, is my approach correct ? :)

\(\sqrt{2} = 1.4\)

\(\sqrt{5}=2.2\)

\(2.2+1.4 = 3.6\)

\((3.6)^2 = 12.96\) apprx \(13\)
Show more

Yes dave13 - that approach is 100% correct!
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
xabi14
User avatar
Joined: 21 Sep 2020
Last visit: 04 Mar 2021
Posts: 4
Posts: 4
Of the following integers which is the closest approximation
Post URL
25 Feb 2021, 21:11
In which circumstances do we use (a+b)^2 = a^2 + 2ab + b^2 rather than a^2 + b^2?
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 10 Sep 2026
Posts: 113,384
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,384
Of the following integers which is the closest approximation
Post URL
25 Feb 2021, 23:19
xabi14
In which circumstances do we use (a+b)^2 = a^2 + 2ab + b^2 rather than a^2 + b^2?
Show more

(a + b)^2 always equals to a^2 + 2ab + b^2. Or did you mean something else?

_________________
New to the GMAT Club?
Signature Read More
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
xabi14
User avatar
Joined: 21 Sep 2020
Last visit: 04 Mar 2021
Posts: 4
Posts: 4
Of the following integers which is the closest approximation
Post URL
26 Feb 2021, 00:50
Bunuel
xabi14
In which circumstances do we use (a+b)^2 = a^2 + 2ab + b^2 rather than a^2 + b^2?

(a + b)^2 always equals to a^2 + 2ab + b^2. Or did you mean something else?
Show more

Thought a^2 + b^2, like a^2 + 2ab + b^2, was also an equivalent to (a+b)^2. That's why i ended up with choice A.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 10 Sep 2026
Posts: 113,384
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,384
Of the following integers which is the closest approximation
Post URL
26 Feb 2021, 00:55
xabi14
Bunuel
xabi14
In which circumstances do we use (a+b)^2 = a^2 + 2ab + b^2 rather than a^2 + b^2?

(a + b)^2 always equals to a^2 + 2ab + b^2. Or did you mean something else?

Thought a^2 + b^2, like a^2 + 2ab + b^2, was also an equivalent to (a+b)^2. That's why i ended up with choice A.
Show more

No.

\((a + b)^2 = (a + b)(a + b) = a^2 + ab + ab + b^2 = a^2 + 2ab + b^2\)


7. Algebra



For more check Ultimate GMAT Quantitative Megathread

Hope it helps.

_________________
New to the GMAT Club?
Signature Read More
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,651
Expert
Expert reply
Posts: 3,651
Of the following integers which is the closest approximation
Post URL
28 Feb 2021, 02:14

Solution



Given
The expression \((√2+√5)^2\)

To find
We need to determine
    • The approximate value of this expression

Approach and Working out

    • \((√2+√5)^2\)
      o \(= (√2)^2 + (√5)^2 + 2(√2) (√5)\) [using the identity \((a+b)^2 = a^2 + b^2 + 2ab\)]
      o = 2 + 5 + 2√10
      o = 7 + 2√10
         √10 is approximately equal to √9, which is equal to 3.
         So, 7 + 2√10 is approximately equal to 7 + 2(3)
          • = 7 + 6
          • = 13

Thus, option C is the correct answer.

Correct Answer: Option C

_________________
Free Trial: Get 25 AI powered videos | 400 practice questions | 8 free webinars

Case studies: How a personalized study plan can save you 60+ hours

MBA admits: M7 admits | INSEAD admits | ISB admits [40+ case studies]


Learn why e-GMAT has 10X more 700+ verified scores than other GMATClub partners – Read our 2000+ reviews
Signature Read More
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
achloes
User avatar
Joined: 16 Oct 2020
Last visit: 19 May 2025
Posts: 243
GMAT 1: 460 Q28 V26
GMAT 2: 550 Q39 V27
GMAT 3: 610 Q39 V35
GMAT 4: 650 Q42 V38
GMAT 5: 720 Q48 V41
GMAT 5: 720 Q48 V41
Posts: 243
Of the following integers which is the closest approximation
Post URL
29 May 2023, 04:32
Because the question says "approximate", that's exactly what I did.

√2 ≈ 1.4
√5 ≈ 2.2

(1.4+2.2)^2 = (3.6)^2

(3.6)^2 must lie between 3^2 and 4^2.

3^2 = 9
4^2 = 16

Also note that 3.6 is closer to 4 than it is to 3. Therefore, (3.6)^2 must also lie closer to 4^2 than it does to 3^2.

Only 13 satisfies this condition. Therefore, C is the answer.
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
nammolestias
User avatar
Joined: 13 Jan 2026
Last visit: 08 Sep 2026
Posts: 65
Location: India
Concentration: Finance, Strategy
Schools: ISB ISB Anderson (UCLA) LBS Bocconi NTU Yale '27 Haas '27 INSEAD Aug '27 CBS '27 Kellogg '27 IIM '27 Anderson '27 LBS '27
GPA: 8.38
WE:Analyst (Finance: Investment Management)
Products:
My Reviews
Schools: ISB ISB Anderson (UCLA) LBS Bocconi NTU Yale '27 Haas '27 INSEAD Aug '27 CBS '27 Kellogg '27 IIM '27 Anderson '27 LBS '27
Posts: 65
Of the following integers which is the closest approximation
Post URL
18 Aug 2026, 16:08
[ltr](2√+5√)2(2+5)2[/ltr]
=2+5+(2*\sqrt{}5*\sqrt{}2)
=7+2*\sqrt{}10..............(2*\sqrt{}10=3)
=7+6
=13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderator:
Bunuel
Math Expert
113384 posts