It is currently 16 Jan 2018, 13:30

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If the sum of the square roots of two integers is

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
4 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43296

Kudos [?]: 139205 [4], given: 12779

If the sum of the square roots of two integers is [#permalink]

Show Tags

New post 30 Oct 2016, 06:36
4
This post received
KUDOS
Expert's post
46
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

75% (01:59) correct 25% (03:12) wrong based on 470 sessions

HideShow timer Statistics

If the sum of the square roots of two integers is \(\sqrt{9+6\sqrt{2}}\), what is the sum of the squares of these two integers?

(A) 40
(B) 43
(C) 45
(D) 48
(C) 52
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 139205 [4], given: 12779

9 KUDOS received
Director
Director
User avatar
P
Joined: 05 Mar 2015
Posts: 962

Kudos [?]: 310 [9], given: 41

Re: If the sum of the square roots of two integers is [#permalink]

Show Tags

New post 30 Oct 2016, 09:00
9
This post received
KUDOS
3
This post was
BOOKMARKED
Bunuel wrote:
If the sum of the square roots of two integers is \(\sqrt{9+6\sqrt{2}}\), what is the sum of the squares of these two integers?

(A) 40
(B) 43
(C) 45
(D) 48
(C) 52

Let nos be x &y
√x + √y= \(\sqrt{9+6\sqrt{2}}\)
sq both sides.
x+y+2√xy=9+6√2
since x & y are integers
x+y=9----------(1)
and 2√xy=6√2
or √xy=3√2
sq both sides to get xy=18-----(2)

sq . both sides (1)
x^2+y^2+2xy=81
x^2+y^2=81-2xy
x^2+y^2=81-36=45---(as xy=18 from (2))

Ans C

Kudos [?]: 310 [9], given: 41

7 KUDOS received
Manager
Manager
User avatar
G
Status: Quant Expert Q51
Joined: 02 Aug 2014
Posts: 65

Kudos [?]: 58 [7], given: 15

Re: If the sum of the square roots of two integers is [#permalink]

Show Tags

New post 30 Oct 2016, 11:18
7
This post received
KUDOS
6
This post was
BOOKMARKED
Let a and b be both of the integers.

\(\sqrt{a}+\sqrt{b}=\sqrt{9+6\sqrt{2}}\)

Lets square both sides of the equation

we get

\(a+b+2\sqrt{a}\sqrt{b}=9+6\sqrt{2}\)

Then

\(a+b= 9\) [1]

\(2\sqrt{a}\sqrt{b}=6\sqrt{2}\) [2]

[2] \(\sqrt{ab}=3\sqrt{2}\) lets square both sides \(ab=18\)

so we get a system

\(a+b=9\)
\(ab=18\)

Combining both equations we get : \(a^2-9a+18=0\)

Solving this second degree equation we get : \(a = 3\) and \(b = 6\)

We are searching for the sum of the squares of these two integers.

so \(a^2+b^2=9+36 = 45\)

So the answer is C.
_________________

My GMAT DATA SUFFICIENCY Course on UDEMY

Kudos [?]: 58 [7], given: 15

2 KUDOS received
Intern
Intern
avatar
B
Joined: 30 Jun 2017
Posts: 2

Kudos [?]: 7 [2], given: 14

Location: India
CAT Tests
If the sum of the square roots of two integers is [#permalink]

Show Tags

New post 17 Jul 2017, 10:57
2
This post received
KUDOS
AnisMURR wrote:
Let a and b be both of the integers.

\(\sqrt{a}+\sqrt{b}=\sqrt{9+6\sqrt{2}}\)

Lets square both sides of the equation

we get

\(a+b+2\sqrt{a}\sqrt{b}=9+6\sqrt{2}\)

Then

\(a+b= 9\) [1]

\(2\sqrt{a}\sqrt{b}=6\sqrt{2}\) [2]

[2] \(\sqrt{ab}=3\sqrt{2}\) lets square both sides \(ab=18\)

so we get a system

\(a+b=9\)
\(ab=18\)

Combining both equations we get : \(a^2-9a+18=0\)

Solving this second degree equation we get : \(a = 3\) and \(b = 6\)

We are searching for the sum of the squares of these two integers.

so \(a^2+b^2=9+36 = 45\)

So the answer is C.



I don't think this method will be helpful in GMAT - where we target a problem not more than 2 min.
Just try this one..
we know that sqaure of integers can only be from terms of the series of 1,4,9,16,25,36,49,64,.......
Further, summation of any two terms from the series should be equal to the one of the options given. It comes out that only 40 (36+4) and 45 (36+9) can be formed from the series of square of integers. By ballparking sqaure root of complex number given comes out to be square root of 18 i.e. slightly more than 4. whereas the summation of sqaure root of 2 & 6 is slightly less than 4 and the summation of sqaure root of 3 & 6 is slightly more than 4. Hence answer is C.

Kudos [?]: 7 [2], given: 14

Manager
Manager
User avatar
G
Status: Quant Expert Q51
Joined: 02 Aug 2014
Posts: 65

Kudos [?]: 58 [0], given: 15

Re: If the sum of the square roots of two integers is [#permalink]

Show Tags

New post 19 Jul 2017, 22:02
Hello Metwing Nice analysis :)

But beleive me it took me less than 2 minutes.

Best,
_________________

My GMAT DATA SUFFICIENCY Course on UDEMY

Kudos [?]: 58 [0], given: 15

Intern
Intern
avatar
B
Joined: 25 Apr 2017
Posts: 12

Kudos [?]: 3 [0], given: 22

Re: If the sum of the square roots of two integers is [#permalink]

Show Tags

New post 02 Aug 2017, 15:17
AnisMURR wrote:
\(a+b=9\)
\(ab=18\)

Combining both equations we get : \(a^2-9a+18=0\)


Please how do you arrive at the above equation from those 2? Can't seem to figure it out. Seems like a step is missing -- as a expert, it is probably obvious to you. But after 30 minutes, I am still clueless.

Kudos [?]: 3 [0], given: 22

3 KUDOS received
Senior Manager
Senior Manager
avatar
G
Joined: 24 Apr 2016
Posts: 334

Kudos [?]: 203 [3], given: 48

Re: If the sum of the square roots of two integers is [#permalink]

Show Tags

New post 02 Aug 2017, 15:36
3
This post received
KUDOS
getitdoneright wrote:
AnisMURR wrote:
\(a+b=9\)
\(ab=18\)

Combining both equations we get : \(a^2-9a+18=0\)


Please how do you arrive at the above equation from those 2? Can't seem to figure it out. Seems like a step is missing -- as a expert, it is probably obvious to you. But after 30 minutes, I am still clueless.


a+b = 9

square both sides

\((a+b)^2 = 9^2\)

\(a^2 + b^2 + 2ab = 81\)

Substituting the value of ab (18) in the above equation

\(a^2 + b^2 + (2*18) = 81\)

\(a^2 + b^2 = 81 - 36 = 45\)

Hope this helps

Kudos [?]: 203 [3], given: 48

Manager
Manager
avatar
B
Joined: 07 Jun 2017
Posts: 109

Kudos [?]: 3 [0], given: 454

Re: If the sum of the square roots of two integers is [#permalink]

Show Tags

New post 02 Aug 2017, 21:00
rohit8865 wrote:
Bunuel wrote:
If the sum of the square roots of two integers is \(\sqrt{9+6\sqrt{2}}\), what is the sum of the squares of these two integers?

(A) 40
(B) 43
(C) 45
(D) 48
(C) 52

Let nos be x &y
√x + √y= \(\sqrt{9+6\sqrt{2}}\)
sq both sides.
x+y+2√xy=9+6√2
since x & y are integers
x+y=9----------(1)
and 2√xy=6√2
or √xy=3√2
sq both sides to get xy=18-----(2)

sq . both sides (1)
x^2+y^2+2xy=81
x^2+y^2=81-2xy
x^2+y^2=81-36=45---(as xy=18 from (2))

Ans C


Dear,
How do you get "x^2+y^2+2xy=81"?
Where is this 81 from?

Thank you so much.

Kudos [?]: 3 [0], given: 454

1 KUDOS received
Manager
Manager
avatar
B
Joined: 19 Aug 2016
Posts: 63

Kudos [?]: 3 [1], given: 1

If the sum of the square roots of two integers is [#permalink]

Show Tags

New post 05 Aug 2017, 16:54
1
This post received
KUDOS
pclawong wrote:
rohit8865 wrote:
Bunuel wrote:
If the sum of the square roots of two integers is \(\sqrt{9+6\sqrt{2}}\), what is the sum of the squares of these two integers?

(A) 40
(B) 43
(C) 45
(D) 48
(C) 52

Let nos be x &y
√x + √y= \(\sqrt{9+6\sqrt{2}}\)
sq both sides.
x+y+2√xy=9+6√2
since x & y are integers
x+y=9----------(1)
and 2√xy=6√2
or √xy=3√2
sq both sides to get xy=18-----(2)

sq . both sides (1)
x^2+y^2+2xy=81
x^2+y^2=81-2xy
x^2+y^2=81-36=45---(as xy=18 from (2))

Ans C


Dear,
How do you get "x^2+y^2+2xy=81"?
Where is this 81 from?

Thank you so much.


In the above equation, we have got x+y=9 (eqn 1)so when u square on both sides u will get
x^2+y^2+2xy=81

Kudos [?]: 3 [1], given: 1

Manager
Manager
User avatar
S
Status: love the club...
Joined: 24 Mar 2015
Posts: 231

Kudos [?]: 28 [0], given: 480

Re: If the sum of the square roots of two integers is [#permalink]

Show Tags

New post 30 Sep 2017, 19:08
Bunuel wrote:
If the sum of the square roots of two integers is \(\sqrt{9+6\sqrt{2}}\), what is the sum of the squares of these two integers?

(A) 40
(B) 43
(C) 45
(D) 48
(C) 52



hi Bunuel

very high quality question this one is indeed. Can you please provide some links to such questions to practice..?

thanks in advance, man

Kudos [?]: 28 [0], given: 480

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43296

Kudos [?]: 139205 [0], given: 12779

Re: If the sum of the square roots of two integers is [#permalink]

Show Tags

New post 01 Oct 2017, 02:59
Expert's post
1
This post was
BOOKMARKED
gmatcracker2017 wrote:
Bunuel wrote:
If the sum of the square roots of two integers is \(\sqrt{9+6\sqrt{2}}\), what is the sum of the squares of these two integers?

(A) 40
(B) 43
(C) 45
(D) 48
(C) 52



hi Bunuel

very high quality question this one is indeed. Can you please provide some links to such questions to practice..?

thanks in advance, man


Roots DS Questions
Roots PS Questions

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 139205 [0], given: 12779

Manager
Manager
User avatar
S
Status: love the club...
Joined: 24 Mar 2015
Posts: 231

Kudos [?]: 28 [0], given: 480

Re: If the sum of the square roots of two integers is [#permalink]

Show Tags

New post 01 Oct 2017, 07:50
Bunuel wrote:
gmatcracker2017 wrote:
Bunuel wrote:
If the sum of the square roots of two integers is \(\sqrt{9+6\sqrt{2}}\), what is the sum of the squares of these two integers?

(A) 40
(B) 43
(C) 45
(D) 48
(C) 52



hi Bunuel

very high quality question this one is indeed. Can you please provide some links to such questions to practice..?

thanks in advance, man


Roots DS Questions
Roots PS Questions

Hope it helps.


thanks man
great you are 8-)

Kudos [?]: 28 [0], given: 480

Manager
Manager
avatar
S
Joined: 19 Aug 2016
Posts: 137

Kudos [?]: 21 [0], given: 56

Location: India
Schools: ISB '20 (WD)
GMAT 1: 610 Q38 V35
GPA: 3.82
Reviews Badge
Re: If the sum of the square roots of two integers is [#permalink]

Show Tags

New post 05 Nov 2017, 11:24
hi Bunuel

very high quality question this one is indeed. Can you please provide some links to such questions to practice..?

thanks in advance, man[/quote][/quote]




Hello,

I'm still unable to understand the solution. Could you please provide the official solution or another explaination to the question?

Thanks
_________________

Consider giving me Kudos if you find my posts useful, challenging and helpful!

Kudos [?]: 21 [0], given: 56

VP
VP
avatar
P
Joined: 22 May 2016
Posts: 1244

Kudos [?]: 454 [0], given: 670

Premium Member CAT Tests
If the sum of the square roots of two integers is [#permalink]

Show Tags

New post 06 Nov 2017, 09:20
Bunuel wrote:
If the sum of the square roots of two integers is \(\sqrt{9+6\sqrt{2}}\), what is the sum of the squares of these two integers?

(A) 40
(B) 43
(C) 45
(D) 48
(C) 52

AnisMURR wrote:
Let a and b be both of the integers.

\(\sqrt{a}+\sqrt{b}=\sqrt{9+6\sqrt{2}}\)

Lets square both sides of the equation

we get

\(a+b+2\sqrt{a}\sqrt{b}=9+6\sqrt{2}\)

Then

\(a+b= 9\) [1]

\(2\sqrt{a}\sqrt{b}=6\sqrt{2}\) [2]

[2] \(\sqrt{ab}=3\sqrt{2}\) lets square both sides \(ab=18\)

so we get a system

\(a+b=9\)
\(ab=18\)

Combining both equations we get : \(a^2-9a+18=0\)

Solving this second degree equation we get : \(a = 3\) and \(b = 6\)

We are searching for the sum of the squares of these two integers.

so \(a^2+b^2=9+36 = 45\)

So the answer is C.

AnisMURR , I can follow everything if I accept this part's last line:
Quote:
\(\sqrt{a}+\sqrt{b}=\sqrt{9+6\sqrt{2}}\)

Lets square both sides of the equation

we get

\(a+b+2\sqrt{a}\sqrt{b}=9+6\sqrt{2}\)

It looks as if you've gotten to a version of a square of a sum (?):
\((a + b)^2 = a^2 + 2ab + b^2\)
Why does (a + b) = 9?
Put another way, why is there not a separate "b" (or analogous b^2?) term?

I think I am missing something really obvious.
_________________

(formerly genxer123)
At the still point, there the dance is. -- T.S. Eliot

Kudos [?]: 454 [0], given: 670

Expert Post
2 KUDOS received
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1820

Kudos [?]: 1044 [2], given: 5

Re: If the sum of the square roots of two integers is [#permalink]

Show Tags

New post 08 Nov 2017, 16:35
2
This post received
KUDOS
Expert's post
Bunuel wrote:
If the sum of the square roots of two integers is \(\sqrt{9+6\sqrt{2}}\), what is the sum of the squares of these two integers?

(A) 40
(B) 43
(C) 45
(D) 48
(C) 52


We can let a = the first integer and b = the second integer. Thus:

√a + √b = √(9 + 6√2)

We are asked to find a^2 + b^2.

Let’s square both sides of the equation above.

(√a + √b)^2 = [√(9 + 6√2)]^2

a + 2√ab + b = 9 + 6√2

Since a and b are integers, we must have:

a + b = 9 and 2√ab = 6√2

If we square both sides of a + b = 9, we have:

a^2 + 2ab + b^2 = 81

If we square both sides of 2√ab = 6√2, we have:

4ab = 36(2)

2ab = 36

We can now substitute 36 for 2ab in a^2 + 2ab + b^2 = 81 to obtain:

a^2 + 36 + b^2 = 81

a^2 + b^2 = 45

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 1044 [2], given: 5

Re: If the sum of the square roots of two integers is   [#permalink] 08 Nov 2017, 16:35
Display posts from previous: Sort by

If the sum of the square roots of two integers is

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.