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(sqrt(9+sqrt(80)) + sqrt(9-sqrt(80)))^2 = ?

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sfbay
 Post subject: (sqrt(9+sqrt(80)) + sqrt(9-sqrt(80)))^2 = ?
 Post Posted: Sat Sep 17, 2011 4:32 pm 
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(sqrt(9+sqrt(80)) + sqrt(9-sqrt(80)))^2 =

from gmat prep 2
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sfbay
 Post subject: Re: (sqrt(9+sqrt(80)) + sqrt(9-sqrt(80)))^2 = ?
 Post Posted: Sun Sep 18, 2011 11:53 am 
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FYI - it is a perfect squares problem but i was hoping to find a better a better/faster/easier way of doing this.
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MannyRosas
 Post subject: Re: (sqrt(9+sqrt(80)) + sqrt(9-sqrt(80)))^2 = ?
 Post Posted: Mon Sep 19, 2011 7:32 am 
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Students


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(sqrt(9+sqrt(80)) + sqrt(9-sqrt(80)))^2=
as a perfect square:
(sqrt(9+sqrt(80))^2 + 2*sqrt(9+sqrt(80))(sqrt(9-sqrt(80)) + sqrt(9-sqrt(80))^2=
9+sqrt(80) + 2*sqrt[(9+sqrt(80))(9-sqrt(80))] + 9-sqrt(80)=
adding the 9s and subtracting the sqrt(80)s:
2*9+2*sqrt[9^2-sqrt(80)^2]=
18+2*sqrt(81-80)=
18+2*1=
20
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RonPurewal
 Post subject: Re: (sqrt(9+sqrt(80)) + sqrt(9-sqrt(80)))^2 = ?
 Post Posted: Tue Sep 20, 2011 7:43 am 
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ManhattanGMAT Staff


Posts: 7146
MannyRosas wrote:
(sqrt(9+sqrt(80)) + sqrt(9-sqrt(80)))^2=
as a perfect square:
(sqrt(9+sqrt(80))^2 + 2*sqrt(9+sqrt(80))(sqrt(9-sqrt(80)) + sqrt(9-sqrt(80))^2=
9+sqrt(80) + 2*sqrt[(9+sqrt(80))(9-sqrt(80))] + 9-sqrt(80)=
adding the 9s and subtracting the sqrt(80)s:
2*9+2*sqrt[9^2-sqrt(80)^2]=
18+2*sqrt(81-80)=
18+2*1=
20


yep.
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sfbay
 Post subject: Re: (sqrt(9+sqrt(80)) + sqrt(9-sqrt(80)))^2 = ?
 Post Posted: Tue Sep 20, 2011 8:25 pm 
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Location: San Francisco
Ron

I know you are not a computer wizard but could those who are add a few buttons on the font ribbon like a sqrt symbol and exp. just tedious to have to put in all those parenthesis and sqrts etc
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RonPurewal
 Post subject: Re: (sqrt(9+sqrt(80)) + sqrt(9-sqrt(80)))^2 = ?
 Post Posted: Thu Oct 06, 2011 5:39 am 
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ManhattanGMAT Staff


Posts: 7146
sfbay wrote:
Ron

I know you are not a computer wizard but could those who are add a few buttons on the font ribbon like a sqrt symbol and exp. just tedious to have to put in all those parenthesis and sqrts etc


yeah, but the cool thing is, now that we have the internet you don't have to worry about that anymore. viz.:
* do a google search for “square root symbol”
* copy
* paste
√ √ √
there you go.
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