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

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(1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

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New post Updated on: 16 Jul 2018, 20:08
7
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A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

55% (02:13) correct 45% (02:25) wrong based on 125 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
Sq.Root.png [ 4.22 KiB | Viewed 1064 times ]

Originally posted by KarthikvsGMAT 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.
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Re: (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

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New post 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
_________________

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


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Re: (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

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New post 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!
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Re: (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

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New post 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!
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Re: (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

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New post 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)
_________________

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


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Re: (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

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New post 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

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Re: (1 + 3^(1/2))(2 + 3^(1/2))^(1/2)  [#permalink]

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