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

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Intern
Status: MBA Student
Joined: 20 Nov 2017
Posts: 30
Location: India
Concentration: Strategy, Marketing
GPA: 3.9
WE: Consulting (Consumer Electronics)
(1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

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Updated on: 16 Jul 2018, 20:08
8
00:00

Difficulty:

75% (hard)

Question Stats:

54% (02:20) correct 46% (02:31) wrong based on 157 sessions

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

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 1656 times ]

Originally posted by KarthikMBA2019 on 16 Jul 2018, 16:24.
Last edited by Bunuel on 16 Jul 2018, 20:08, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Aug 2009
Posts: 7764
Re: (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

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16 Jul 2018, 19:32
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
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Joined: 27 Dec 2016
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Re: (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

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01 Sep 2018, 18:37
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: 332
Re: (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

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01 Sep 2018, 18:38
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: 7764
Re: (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

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01 Sep 2018, 19:15
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)
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Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
Re: (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

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01 Sep 2018, 19:46
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: 332
Re: (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

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02 Sep 2018, 14:16
Thank You chetan2u & PKN
Re: (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)   [#permalink] 02 Sep 2018, 14:16
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