GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 09 Dec 2018, 12:14

### 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

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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free GMAT Algebra Webinar

December 09, 2018

December 09, 2018

07:00 AM PST

09:00 AM PST

Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
• ### Free lesson on number properties

December 10, 2018

December 10, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

# (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)

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

### Hide Tags

Intern
Joined: 20 Nov 2017
Posts: 28
Location: India
GRE 1: Q158 V150
GPA: 3.9
WE: Consulting (Consumer Electronics)
(1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

### Show Tags

Updated on: 16 Jul 2018, 19:08
8
00:00

Difficulty:

85% (hard)

Question Stats:

56% (02:12) correct 44% (02:35) wrong based on 148 sessions

### HideShow timer Statistics

$$(1 + \sqrt{3})\sqrt{2 + \sqrt{3}}$$

A. $$\sqrt{2}(2 - \sqrt{3})$$

B. $$\sqrt{2}(2 + \sqrt{2})$$

C. $$\sqrt{2}(2 + \sqrt{3})$$

D. $$\sqrt{2}(3 + \sqrt{3})$$

E. $$\sqrt{3}(2 + \sqrt{3})$$

Attachment:

Sq.Root.png [ 4.22 KiB | Viewed 1390 times ]

Originally posted by KarthikvsGMAT on 16 Jul 2018, 15:24.
Last edited by Bunuel on 16 Jul 2018, 19:08, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Aug 2009
Posts: 7095
Re: (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

### Show Tags

16 Jul 2018, 18:32
2
1
Karthik200 wrote:
$$(1 + \sqrt{3})\sqrt{(2 + [square_root]3})[/square_root]$$

A. $$\sqrt{2}(2 - \sqrt{3})$$
B. $$\sqrt{2}(2 + \sqrt{2})$$
C. $$\sqrt{2}(2 + \sqrt{3})$$
D. $$\sqrt{2}(3 + \sqrt{3})$$
E. $$\sqrt{3}(2 + \sqrt{3})$$

Guys, sorry for the poor question formatting. I tried my best to make it proper. However, the square root inside the square root is somehow not appearing properly. Kindly, use the attachment to view the question.

Let x be the value of the equation..
$$X=(1+√3)(\sqrt{2+√3})$$...
So $$x^2=(1+3+2√3)(2+√3)=(4+2√3)(2+√3)=2(2+√3)(2+√3)=2(2+√3)^2$$..
Therefore x=√2*(2+√3)

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Senior Manager
Joined: 27 Dec 2016
Posts: 253
Re: (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

### Show Tags

01 Sep 2018, 17:37
chetan2u wrote:
Karthik200 wrote:
$$(1 + \sqrt{3})\sqrt{(2 + [square_root]3})[/square_root]$$

A. $$\sqrt{2}(2 - \sqrt{3})$$
B. $$\sqrt{2}(2 + \sqrt{2})$$
C. $$\sqrt{2}(2 + \sqrt{3})$$
D. $$\sqrt{2}(3 + \sqrt{3})$$
E. $$\sqrt{3}(2 + \sqrt{3})$$

Guys, sorry for the poor question formatting. I tried my best to make it proper. However, the square root inside the square root is somehow not appearing properly. Kindly, use the attachment to view the question.

Let x be the value of the equation..
$$X=(1+√3)(\sqrt{2+√3})$$...
So $$x^2=(1+3+2√3)(2+√3)=(4+2√3)(2+√3)=2(2+√3)(2+√3)=2(2+√3)^2$$..
Therefore x=√2*(2+√3)

C

Hi Chetan,

I was wondering could you please explain how you went from 2(2+√3)^2 to √2*(2+√3)? Would greatly appreciate it!
Senior Manager
Joined: 27 Dec 2016
Posts: 253
Re: (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

### Show Tags

01 Sep 2018, 17:38
chetan2u wrote:
Karthik200 wrote:
$$(1 + \sqrt{3})\sqrt{(2 + [square_root]3})[/square_root]$$

A. $$\sqrt{2}(2 - \sqrt{3})$$
B. $$\sqrt{2}(2 + \sqrt{2})$$
C. $$\sqrt{2}(2 + \sqrt{3})$$
D. $$\sqrt{2}(3 + \sqrt{3})$$
E. $$\sqrt{3}(2 + \sqrt{3})$$

Guys, sorry for the poor question formatting. I tried my best to make it proper. However, the square root inside the square root is somehow not appearing properly. Kindly, use the attachment to view the question.

Let x be the value of the equation..
$$X=(1+√3)(\sqrt{2+√3})$$...
So $$x^2=(1+3+2√3)(2+√3)=(4+2√3)(2+√3)=2(2+√3)(2+√3)=2(2+√3)^2$$..
Therefore x=√2*(2+√3)

C

Hi Chetan,

I was wondering could you please explain how you went from 2(2+√3)^2 to √2*(2+√3)? Would greatly appreciate it!
Math Expert
Joined: 02 Aug 2009
Posts: 7095
Re: (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

### Show Tags

01 Sep 2018, 18:15
1
csaluja wrote:
chetan2u wrote:
Karthik200 wrote:
$$(1 + \sqrt{3})\sqrt{(2 + [square_root]3})[/square_root]$$

A. $$\sqrt{2}(2 - \sqrt{3})$$
B. $$\sqrt{2}(2 + \sqrt{2})$$
C. $$\sqrt{2}(2 + \sqrt{3})$$
D. $$\sqrt{2}(3 + \sqrt{3})$$
E. $$\sqrt{3}(2 + \sqrt{3})$$

Guys, sorry for the poor question formatting. I tried my best to make it proper. However, the square root inside the square root is somehow not appearing properly. Kindly, use the attachment to view the question.

Let x be the value of the equation..
$$X=(1+√3)(\sqrt{2+√3})$$...
So $$x^2=(1+3+2√3)(2+√3)=(4+2√3)(2+√3)=2(2+√3)(2+√3)=2(2+√3)^2$$..
Therefore x=√2*(2+√3)

C

Hi Chetan,

I was wondering could you please explain how you went from 2(2+√3)^2 to √2*(2+√3)? Would greatly appreciate it!

$$x^2=2(2+√3)^2=(√2)^2*(2+√3)^2.........x*x=(√2*√2)(2+√3)(2+√3)=√2*(2+√3)*√2*(2+√3)...$$
Thus x=√2(2+√3)
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

### Show Tags

01 Sep 2018, 18:46
1
csaluja wrote:
chetan2u wrote:
Karthik200 wrote:
$$(1 + \sqrt{3})\sqrt{(2 + [square_root]3})[/square_root]$$

A. $$\sqrt{2}(2 - \sqrt{3})$$
B. $$\sqrt{2}(2 + \sqrt{2})$$
C. $$\sqrt{2}(2 + \sqrt{3})$$
D. $$\sqrt{2}(3 + \sqrt{3})$$
E. $$\sqrt{3}(2 + \sqrt{3})$$

Guys, sorry for the poor question formatting. I tried my best to make it proper. However, the square root inside the square root is somehow not appearing properly. Kindly, use the attachment to view the question.

Let x be the value of the equation..
$$X=(1+√3)(\sqrt{2+√3})$$...
So $$x^2=(1+3+2√3)(2+√3)=(4+2√3)(2+√3)=2(2+√3)(2+√3)=2(2+√3)^2$$..
Therefore x=√2*(2+√3)

C

Hi Chetan,

I was wondering could you please explain how you went from 2(2+√3)^2 to √2*(2+√3)? Would greatly appreciate it!

Hi csaluja,

Here $$x^2=2*(2+√3)^2$$ (I hope you are clear till this point)
Taking square root both sides, we have
$$\sqrt{x^2}=\sqrt{2*(2+√3)^2}=\sqrt{2}*\sqrt{(2+√3)^2}$$
(You know $$\sqrt{a*b}=\sqrt{a}*\sqrt{b}$$)
Or, $$x=\sqrt{2}*(2+√3)$$
Hope it helps.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Senior Manager
Joined: 27 Dec 2016
Posts: 253
Re: (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

### Show Tags

02 Sep 2018, 13:16
Thank You chetan2u & PKN
Re: (1 + 3^(1/2))(2 + 3^(1/2))^(1/2) &nbs [#permalink] 02 Sep 2018, 13:16
Display posts from previous: Sort by

# (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)

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

 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®.